The State Department on Wednesday labeled allegations made by Russian President Vladimir Putin against Americans earlier this week "absolutely absurd," but stopped short of saying the United States would refuse to assist Russian efforts to question individuals in the U.S.

Earlier in the day, White House press secretary Sarah Sanders said President Donald Trump discussed the possibility of some sort of U.S.-Russia interrogation-swap with Putin during their meeting in Helsinki on Monday.

On Friday, while Trump was visiting the United Kingdom, special counsel Robert Mueller's team obtained new indictments from a federal grand jury charging 12 Russian intelligence officials with hacking Democrats and stealing voters' information.

And just a day after Trump and Putin met, a spokesman for Russia's attorney general released a list of former U.S. officials and private citizens who Russia said it wants to interview about their supposed "crimes" against the Russian state, including former U.S. Ambassador to Russia Michael McFaul.

On Wednesday, Sanders said that while the topic of Mueller potentially going to Russia, and Russian investigators potentially coming to the United States, did come up with Putin, "there wasn't a commitment made on behalf of the United States."

She added: "The president will work with his team, and we'll let you know if there's an announcement on that front."

Less than an hour later, State Department spokeswoman Heather Nauert was pressed by journalists as to why the State Department wouldn't simply reject Russia's "proposal" out-of-hand.

"I can't answer on behalf of the White House," she said. "But what I can tell you is that the overall assertions that have come out of the Russian government are absolutely absurd. The fact that they want to question 11 American citizens and the assertions that the Russian government is making ... we do not stand by those assertions."

Nauert also said that some of the authority for investigative or law enforcement decisions would likely belong to the Department of Justice. "I would have to loop in the DOJ," she said. "This is something that just came out, so I would just tell you that Russian assertions are absolutely absurd at this point."

The "assertions" largely boil down to accusations that U.S. officials assisted Bill Browder, a UK citizen and financier, to avoid paying taxes on money he made in Russia through his venture capital firm, Hermitage Capital.

As Putin put it on Monday, "We have a solid reason to believe that some intelligence officers accompanied and guided these transactions," apparently referring to alleged transactions that Browder made. "So we have an interest of questioning them."

What "solid reason" this might be, however, was far from clear on Wednesday.

For example, the Kremlin banned McFaul from entering Russia in 2014 because of his alleged “active participation in the destruction of the bilateral relationship [between Russia and the United States] and relentless lobbying in favor of a campaign to pressure Russia.”

The real reason for the breakdown in the U.S.-Russia relationship, however, was not McFaul, but Russia's illegal annexation of the Ukrainian region of Crimea earlier that year, and its ongoing campaign to arm rebels and mercenaries in Eastern Ukraine.

The conflicting messages coming from Moscow and Washington are the latest diplomatic headache for Secretary of States Pompeo after a week widely viewed as a low-point for Trump in terms of both U.S. influence abroad and some of America's strongest alliances.

In his joint press conference alongside Putin on Monday in Helsinki, Trump refused to say he believed his own administration's intelligence services, which have unanimously agreed that the Russian government waged an influence campaign during the 2016 election and showed a clear preference for Trump over Democrat Hillary Clinton.

Putin and the Kremlin have denied interfering in the 2016 election, as well as colluding with the Trump campaign. Asked if he believed Russia or the U.S. intelligence community, Trump said he has "confidence in both parties" and suggested Russia had no reason to meddle.

"My people came to me, [Director of National Intelligence] Dan Coats came to me and some others. They said they think it’s Russia. I have President Putin, he just said it’s not Russia," Trump said.

"I will say this. I don’t see any reason why it would be," Trump said, adding that he wanted to see the Democrats' servers and telling reporters "President Putin was extremely strong and powerful in his denial today."

At the White House more than than 24 hours later, Trump said he misspoke in Helsinki, and he meant to say the opposite of what he said at the time.

"The sentence should have been, 'I don't any reason why it wouldn't be Russia.' Sort of a double-negative," Trump said.

In a series of tweets after leaving Finland, Trump touted the meeting as a "great success."

Trump tweet The meeting between President Putin and myself was a great success, except in the Fake News Media!