Secretary Blinken told reporters after his conversation with his Russian counterpart "We had a frank and direct conversation. I pressed the Kremlin to accept the substantial proposal that we put forward."
The top US diplomat declined to characterize Lavrov's reaction, saying, "I can't give you an assessment of whether I think things are any more or less likely."
"But it was important that he heard directly," Blinken said.
The proposal reportedly includes swapping the two Americans, basketball star Brittney Griner and former Marine Paul Whelan, whose plight has drawn growing attention, for convicted Russian arms smuggler Viktor Bout.
The telephone conversation was the first between Blinken and Lavrov since February 15, when the top US diplomat warned Russia against invading Ukraine.
In this call, Blinken said he also pressed Lavrov on Russia honoring a Turkish-brokered proposal to ship grain out of Ukraine and on purported plans by Moscow to annex additional parts of Ukraine seized by Russian troops.
Blinken said he told Lavrov that "the world will never recognize annexation" and that Russia would be hit by additional ramifications.
Blinken said Russia was preparing "sham referendums" to try to "falsely demonstrate that the people in these parts of Ukraine somehow seek to become part of Russia."
"It was very important that the Russians hear directly from us that that will not be accepted -- and not only will it not be accepted, it will result in additional significant costs being imposed upon Russia," Blinken said.
Griner was arrested in February when customs found cannabis oil in her luggage when she arrived in Russia. Whelan was convicted of espionage and given a 16 year sentence.
Viktor Bout was convicted and imprisoned in the United States for his role as an international arms dealer and smuggler.
