"We're working hard to see what we can do to get another proposal that might be more successful," National Security Council spokesman John Kirby told reporters.
The State Department said earlier this month that Russia rejected a "substantial" proposal to free the two Americans -- Wall Street Journal correspondent Evan Gershkovich and Paul Whelan, a former Marine.
Russian President Vladimir Putin later said that he hoped for a solution but that the United States needed to "make a decision that will suit the Russian Federation."
Kirby said the United States "did in recent days put forward a serious proposal. The Russians rebuffed it, regardless of what Mr Putin says."
Gershkovich, 32, was arrested during a reporting trip at the end of March in the Urals city of Yekaterinburg. He is the first Western journalist accused of spying -- a charge he and his employer vigorously deny -- since the Soviet era.
Whelan, 53, was working in security for a US vehicle parts company when he was arrested in Moscow in 2018. He is serving a 16-year sentence for spying, a charge the US government says is without merit.
In an interview with the BBC released Wednesday, Whelan accused the US government of having "just left me in the dust."
"They've basically abandoned me here," he told the BBC by phone. "I'm extremely concerned."
In November, Whelan's family said he had been "hit in the face" by a prisoner, breaking his glasses.
Asked about the interview, Kirby said it was "very, very troubling" that Whelan would be "under physical threat."
"We'll continue to work hard through our embassy in Moscow to make sure he gets consular access and that we can address these direct concerns with our Russian counterparts," Kirby said.
The United States on Wednesday carried out a prisoner swap with Venezuela, with 10 Americans returning in return for an ally of President Nicolas Maduro.
