Asked by a Fox reporter whether he has ever worked for Russia, Mr Trump hit back, saying it was the “most insulting thing I’ve ever been asked”.
He did not provide a clear yes, or no answer.
“I have a one-on-one meeting with Putin like I do with every other leader. I have many one-on-one, nobody ever says anything about it.”
“But with Putin, they say “oh, what did they talk about?”
Democrats are now vowing to use their newly-won control of the House of Representatives to gain information on the interpreters, including the one who sat in on a controversial meeting with Mr Trump and Mr Putin in Helsinki last year.
New house Intelligence Committee chairman Adam Schiff signalled on Sunday that he would move on the interpreter in Finland.
“Last year, we sought to obtain the interpreter’s notes or testimony, from the private meeting between Trump and Putin,” Mr Schiff wrote in a Tweet on Sunday [Monday AEDT].
“The Republicans on our committee voted us down. Will they join us now?
“Shouldn’t we find out whether our president is really putting ‘America first’?”
Separately, ABC News reported that lawyers for the intelligence committee will meet on Monday to look at subpoenaing the interpreters.
ABC reporter Tara Palmeri wrote many Democrats were previously opposed because it’s an unprecedented step that could impact future diplomacy but are now warming to it following the report in The Washington Post report.
Another wave of headlines about Mr Trump’s Russia relationship sets up a long week for the president, who is still considering whether to call a national emergency on the US southern border to build a wall and break the shutdown deadlock.
Around 800,000 federal workers have been furloughed around the nation during a shutdown now headed towards a fourth week.
The standoff was triggered by Democrat refusal to agree to Mr Trump’s demands for $US5.7 billion ($8 billion) in funding for the structure.
The president insists the money is needed to address what he and Republicans have portrayed as a crisis of illegal immigration on the southern border.
More Americans blame Mr Trump and Republicans in Congress than Democrats for the record-breaking government shutdown, according to a Washington Post-ABC News poll released on Sunday.
Some 53 per cent said Mr Trump is mainly at fault, with 29 per cent blaming the Democrats in Congress.
The findings mirror past shutdowns, when the president of the day tends to wear most of the blame.
Despite blame falling on the White House, signs of a breakthrough are scarce, stoking suggestions the shutdown could run through to February. One ominous sign was that Mr Trump cancelled his attendance at the World Economic Forum in Davos next week in Switzerland.