WASHINGTON — Secretary of State Antony J. Blinken said on Thursday that President Biden would “likely” speak directly with President Vladimir V. Putin of Russia “in the near future,” as part of a frantic diplomatic effort to head off what Western officials fear could be a Russian invasion of Ukraine.

Mr. Blinken spoke to reporters in Stockholm on Thursday, shortly after meeting with Russia’s foreign minister, Sergey V. Lavrov, on the sidelines of an annual meeting of the Organization for Security and Cooperation in Europe.

Mr. Blinken said he had communicated “clearly and directly” to Mr. Lavrov American concerns about unusual troop movements and other menacing actions by Moscow that appear to presage a Russian invasion of its neighbor, a former Soviet republic whose independence and Western ties Mr. Putin resents.

Mr. Blinken warned that the United States would work with allies “to impose severe costs and consequences on Russia if it takes further aggressive action against Ukraine.” He said those could include “high-impact economic measures that we’ve refrained from taking in the past,” but declined to offer more details.

Mr. Lavrov came bearing his own threats. Echoing recent warnings by Mr. Putin, Mr. Lavrov said that “drawing Ukraine into the geopolitical games of the United States against the background of the deployment of NATO forces in the immediate vicinity of our borders will have the most serious consequences,” according to a statement from the Russian Foreign Ministry after his meeting with Mr. Blinken.

Mr. Lavrov repeated Mr. Putin’s demand for “long-term security guarantees” on Russia’s western borders, which the Russian president on Wednesday defined as agreements that Ukraine will never join NATO and that the alliance’s weapons systems will not be based there. Mr. Lavrov said that otherwise, Russia was prepared to take “retaliatory measures to correct the military-strategic balance,” according to the statement.

As Russia speaks increasingly of threats from NATO, Mr. Blinken has warned that Russia might fabricate a provocation to justify military action against Ukraine. On Thursday he told reporters that “despite a massive Russian disinformation campaign, Ukraine in no way poses a threat to Russia.”

“The only threat is that of renewed Russian aggression towards Ukraine,” Mr. Blinken said.

Neither Mr. Blinken nor the White House provided more detail on any Biden-Putin conversation. Kremlin officials have suggested the possibility for days, but Mr. Blinken’s remark was the first clear indication from Washington that Mr. Biden was taking the idea seriously.

The two presidents met in person for the first time in June amid a similar state of alarm about a potential Russian invasion of eastern Ukraine, where Russian forces have long backed a pro-Moscow separatist insurgency. Russia annexed Ukraine’s Crimean Peninsula in 2014 in a move the U.S. still does not recognize.

Russian forces partially withdrew shortly before Mr. Biden and Mr. Putin met in Geneva, leading some analysts to suggest that Mr. Putin had manufactured the crisis in part to secure a meeting with the new American president.

Biden officials said at the time that the summit’s goal was in large measure to regain a more stable and predictable footing with the Kremlin. But the relationship remains poisoned.

In brief remarks to reporters before meeting privately with Mr. Blinken, Mr. Lavrov also alluded to a tit-for-tat with the United States involving diplomatic staff. On Wednesday, Russia ordered American diplomats who had been in Moscow for more than three years to fly out of the country by Jan. 31. The move came days after Russia’s ambassador to Washington said that 27 Russian diplomats and their families were being forced to leave the United States by the end of January.

In a daily briefing on Thursday, the State Department’s deputy spokeswoman, Jalina Porter, said the Russian diplomats must leave the country under a policy that limits them to three-year stays. “What’s happening is not an expulsion,” she said, adding that new diplomats may take their place.

The U.S. diplomatic presence in Russia has dramatically reduced over the past few years amid rising tensions between Washington and Moscow. The State Department closed its last two consulates in Russia a year ago, citing a cap on diplomatic employees imposed by Moscow after a round of U.S. sanctions in 2018.

Even as he managed the crisis along Ukraine’s eastern border, Mr. Blinken was also managing diplomacy related to Iran’s nuclear program, as a new round of talks continued in Vienna with little apparent progress. The talks are aimed at restoring the 2015 Iran nuclear deal, which President Donald J. Trump abandoned in 2018.

Mr. Blinken fielded an unusual call on Thursday from the Israeli prime minister, Naftali Bennett, who told him that Iran was engaging in “nuclear blackmail” and called for “an immediate cessation of negotiations” in Vienna.

Mr. Blinken downplayed the call, saying that he and Mr. Bennett had a positive conversation and agreed on the goal of preventing Iran from obtaining nuclear weapons.

He added that Iran’s recent rhetoric and steps to accelerate its nuclear program “don’t give us a lot of cause for optimism,” but said “it is not too late for Iran to reverse course.”

Anton Troianovski contributed reporting from Moscow.