KYIV, Ukraine — Secretary of State Antony J. Blinken on Wednesday said that when he meets with his Russian counterpart on Friday, he would not provide the written response to Russia’s demands on Eastern European security that the Kremlin says it expects.

At the same time, Mr. Blinken warned that President Vladimir V. Putin of Russia was poised to strike quickly against Ukraine.

“We know that there are plans in place to increase that force even more on very short notice,” he said, “and that gives President Putin the capacity, also on very short notice, to take further aggressive action against Ukraine.”

The written response has been one of Moscow’s central requests, and the failure to provide one on Friday could frustrate Russia as Mr. Blinken sits down in Geneva with Russia’s foreign minister, Sergey V. Lavrov. The meeting may be one of the last chances for a diplomatic path to averting what U.S. officials fear is an imminent Russian attack on Ukraine.

Moscow has said repeatedly that it would not let the U.S. drag out negotiations without providing responses to Russia’s demands. Hours before Mr. Blinken spoke, the Kremlin spokesman, Dmitri S. Peskov, said that Russia was awaiting a written response to its proposals, according to the Tass news service. It is still possible the U.S. will provide written responses to Russia’s demands in the days after the meeting on Friday.

Russia is already supporting separatists in a conflict in eastern Ukraine, but U.S. officials fear that Mr. Putin may seek to invade and occupy more of the country if his demands are not met. Those demands include a halt on further NATO expansion into Eastern Europe and a legally binding pledge from NATO that it would never admit Ukraine as a member. The United States has called those positions unacceptable.

Mr. Blinken seemed to suggest that, by taking positions the West considers “absolute non-starters,” Russia was making it hard to discern what it actually thinks it can achieve through diplomacy.

“It’s not clear what Russia’s central demand is,” Mr. Blinken said. “I think we’ll have a better idea, maybe, after Friday.”

Mr. Blinken made the remarks at Ukraine’s foreign ministry after a meeting with his counterpart, Dmytro Kuleba. He met earlier in the day with the country’s president, Volodymyr Zelensky, in the latest show of support by the Biden administration.

Both Russian and American officials sounded a pessimistic note after three rounds of talks last week, with one Russian diplomat saying that talks with the West were approaching a “dead end,” and Mr. Blinken offered little reason for optimism.

Mr. Blinken said the United States did not make any formal proposals last week but merely “talked about areas” for reciprocal cooperation, including arms control and the conduct of military exercises in Europe.

He said it was unclear whether Russia was prepared to negotiate in good faith on those fronts, or at all.

Russia has positioned around 100,000 troops along its western border with Ukraine, although precise estimates vary. On Tuesday, the White House press secretary, Jen Psaki, said that Russia “could at any point launch an attack in Ukraine.”

In a news conference on Wednesday, President Biden echoed that message, saying he expected Mr. Putin to invade. “Do I think he’ll test the West, test the United States and NATO, as significantly as he can? Yes, I think he will,” Mr. Biden told reporters, adding: “But I think he will pay a serious and dear price for it that he doesn’t think now will cost him what it’s going to cost him. And I think he will regret having done it.”

Speaking at a forum in Moscow earlier on Wednesday, Russia’s deputy foreign minister, Sergei A. Ryabkov, repeated his government’s previous denial that Moscow has any plans to move its forces into Ukraine.

“We will not attack, strike, invade, quote unquote, whatever, Ukraine,” Mr. Ryabkov said. He said the Russian troops near Ukraine’s border were conducting training exercises.

After meeting with Mr. Blinken in the morning, Mr. Zelensky, Ukraine’s president, appeared to flaunt Mr. Putin’s warnings that Ukraine must not be allowed to join NATO. During brief remarks alongside Mr. Blinken, Mr. Zelensky said that American military support for his country affirms “our strategic plans for Ukraine’s accession to the alliance.”

In 2008, NATO declared in a statement that Ukraine would someday join the 30-member security pact, infuriating Mr. Putin. Western officials say that it would be impractical for Ukraine to become a member in the foreseeable future but that they will not adjust their position in response to Russian threats.

It was unclear whether Mr. Blinken promised Mr. Zelensky and Mr. Kuleba any specific new measures of support to deter Moscow, or to fight Russia’s military in the event of a full-scale invasion. But a State Department official on Wednesday confirmed reports that the Biden administration last month approved an additional $200 million in defensive security aid for Ukraine. That money comes in addition to $450 million in such aid the United States provided Ukraine in the last fiscal year.

The Biden administration has warned that Russia will suffer massive economic sanctions imposed by Washington and its European allies if Mr. Putin moves militarily against Ukraine, though many analysts doubt that he can be deterred by such measures.

Although Mr. Blinken downplayed the likelihood of any breakthrough Friday with Mr. Lavrov, a wily, veteran negotiator, he said the United States was determined to pursue a diplomatic solution to the crisis. He plans to stop on Thursday in Berlin to meet with German officials, and attend a group session with French and British diplomats also in attendance.

Mr. Blinken declined to provide details of the U.S. security assistance to Kyiv, which has asked for more powerful weapons to combat Russian forces. U.S. officials say any Russian attack is likely to come in the next several weeks, before the spring thaw makes for muddy conditions that would ensnare heavy vehicles.

Later on Wednesday, Mr. Zelensky addressed the nation in a video encouraging Ukrainians to remain calm and, in contrast to the urgency conveyed by the United States, said the country faced no greater threat today than it has over the past years of war.

“What is the news?” Mr. Zelensky said. “Hasn’t this been the reality for eight years already? Didn’t the invasion start in 2014? Did the threat of full-scale war really appear just now?” He said the risk of war “hasn’t increased,” though this contrasted sharply with what Mr. Blinken had said earlier in the day.

During his visit to the U.S. embassy, Mr. Blinken discussed contingency plans to ensure the safety of its staff and families, according to the State Department. But he would not say, in response to a later question, when President Biden might announce a nominee for the still-vacant post of U.S. ambassador to Ukraine.

Mr. Blinken welcomed the American search for a diplomatic solution but described it as walking a perilous diplomatic line. Offering nothing to Russia poses risks, while offering too much does as well, he said.

He summed up Russia’s negotiating position as, “hand over Ukraine to our sphere of influence, or we will end Ukraine as it is. Those are the stakes.” Gen. Ben Hodges, the former commander of the United States Army in Europe, said he had not seen such a flurry of American diplomatic activity since the war in the Balkans.

“I’ve never seen such an intensive and comprehensive U.S. diplomatic effort, at least not since 1995 and the Dayton Peace Accords,” he said in an interview. “I don’t agree with everything the administration is doing, but they’ve made the effort necessary to bring along allies and keep them there.”

Even so, he said, he is more pessimistic about the prospect of military escalation than he has been in months.

“I think Putin has put himself in a corner; he’s going to have to show something for this,” he said.

After Mr. Kuleba and Mr. Blinken made their joint remarks, the Ukrainian minister provided his American visitor with a brief tour of an exhibit in the lobby of the grand foreign ministry building detailing its architectural origins under the Soviet leader Josef Stalin.

It was a reminder of the sometimes dark historical ties between Kyiv and Moscow. The foreign ministry structure was first planned in the 1930s, “a woeful epoch when Stalin and those around him committed genocide against the Ukrainian people,” a placard explained.

Mr. Kuleba also spoke by phone on Wednesday with Josep Borrell Fontelles, the European Union’s top diplomat, about economic sanctions the bloc could impose on Russia and additional financial support for Ukraine, the Ukrainian foreign ministry said.

“Every country in the European Union should understand that, though the price of deterring Russia is high, the cost of stopping a new war will be higher” if it starts, Mr. Kuleba said after the call, local media reported.

Michael Schwirtz contributed reporting from Kyiv, and Anton Troianovski from Moscow.