The individuals are related to Russia's case against the financier Bill Browder, a fierce Putin critic who was instrumental in the United States imposing sanctions in 2012 on top Russian officials accused of corruption. "We're not going to have it, and that's the way it's going to be", Trump said.
Browder said he is "confident" that Trump will not allow the offer to go through in the end.
The US leader's embrace of Putin this week drew derision and outrage across the US political spectrum.
But the US leader declined to say whether he thinks Putin is lying in saying he did not meddle in Trump's 2016 campaign to help him defeat Democrat Hillary Clinton, an outcome Putin said he wanted to happen.
It comes just days after Trump and Putin met in Helsinki for their first official summit on Monday. "But I have confidence in both parties", Mr. Trump said as Putin stood at a podium by his side.
Just last month, TIME's editors made headlines with a cover that depicted Trump looming over a crying immigrant girl in a now-famous image.
Earlier Wednesday, Trump appeared to answer "no" when asked whether Russian Federation was still targeting the United States.
Trump categorically denied the possibility that Russian Federation may have interfered in the election, to the outrage of a number of Americans.
"But you haven't condemned Putin specifically", Glor responded. "Because there is no rule of law, as I said, in Russian Federation".
The White House had said Wednesday it was under consideration, even though the State Department called Russia's allegations against the Americans "absurd".
Trump then told reporters on Wednesday he didn't believe Russian Federation was still targeting the U.S. But White House press secretary Sarah Huckabee Sanders said later that he does believe that Russian Federation may try to target U.S. elections again and the "threat still exists". He cited US sanctions and the expulsion of alleged Russian spies from the USA, telling reporters that Putin "understands it, and he's not happy about it".
During a Wednesday evening segment about Trump's latest dust-up, the network ran a chyron reading: "Try, try again: White House and Trump offer different responses on Russian Federation".
Meantime, Trump also threatened "tremendous retribution" if his planned meeting with European Commission officials next week in Washington fails to produce a trade deal he deems fair on automobiles.
He then posted a video from Fox News showcasing previous occasions on which he had acknowledged that Russian Federation had meddled in the election. Rather, she contended, the president said "no" to reporters' desire to ask questions. The Russian President suggested special counsel Robert Mueller's investigators could come to Russia to question the two dozen Russians that have been charged with interfering in the 2016 presidential election.
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