President Donald Trump said he'd "love to" run for re-election in 2020 against President Barack Obama's vice president, Joe Biden.

"I dream, I dream about Biden. That's a dream," Trump said when asked which Democrat he believes he'll face in the next presidential race during a CBS News interview that aired Wednesday.

"Look, Joe Biden ran three times. He never got more than 1 percent and President Obama took him out of the garbage heap, and everybody was shocked that he did," Trump said. "I'd love to have it be Biden."

Trump added, however, that he would be fine running against any of the "group of seven or eight" Democrats and other politicians who might be considering presidential runs — such as Sens. Elizabeth Warren, D-Mass., Bernie Sanders, I-Vt., Kamala Harris, D-Calif., and Kirsten Gillibrand, D-N.Y.

Biden's nonprofit, the Biden Foundation, did not immediately respond to CNBC's request for comment.

Trump's confidence toward his potential challengers comes amid a cycle of harsh bipartisan criticism of his performance at a summit Monday with Russian President Vladimir Putin in Helsinki, Finland.

Following a closed-door, one-on-one meeting with Putin, Trump spoke at a joint press conference with the Russian leader. During that briefing, he refused to say unequivocally that he believed U.S. intelligence reports stating that Russia interfered in the 2016 election. He appeared to put more trust in Putin, whose denial of any meddling he called "extremely strong and powerful."

He also said "I don’t see any reason why it would be" Russia that hacked Democrats during the 2016 campaign, and suggested that the U.S. and Russia were both responsible for the nations' strained relationship.

In a statement following the summit, Biden joined the chorus of bipartisan criticism against Trump, saying on Monday that the president "insulted our friends and made common cause with our adversaries."

Biden's statement continued: "He embraced our number one adversary, blamed America rather than Russian aggression for the deterioration in our bilateral relations, trashed his own justice department, and put Putin’s word above that of our own intelligence community whose leaders he appointed."

On Tuesday, Trump walked back one of his remarks, saying he misspoke and meant to say he saw no reason "why it wouldn't be Russia."

"Sort of a double negative," he said.

In the CBS interview, Trump said it was "true" that Russia meddled in the election and said he would hold Putin responsible for that interference "because he's in charge of the country."