South Bend, Ind., Mayor Pete Buttigieg Pete ButtigiegBillionaire who donated to Trump in 2016 donates to Biden The Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November Buttigieg stands in as Pence for Harris's debate practice MORE, a Democratic presidential hopeful, is walking back previous comments he made saying the Democratic primary could turn into a two-way race between him and Sen. Elizabeth Warren Elizabeth WarrenOvernight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds On The Money: Half of states deplete funds for Trump's 0 unemployment expansion | EU appealing ruling in Apple tax case | House Democrats include more aid for airlines in coronavirus package Warren, Khanna request IG investigation into Pentagon's use of coronavirus funds MORE (D-Mass.) after facing criticism from other contenders in the race.

"I don’t remember the exact context," Buttigieg told reporters in Iowa on Saturday, referring to comments he originally made on Showtime's "The Circus" indicating that he saw the large Democratic field shrinking to a “two-way” race between himself and the Massachusetts senator.

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The mayor on Saturday added that he did not think the comments came out right before emphasizing the strength of the other contenders in the race.

"Look, the bottom line is this is a really strong competition among really strong campaigns," he said.

Buttigieg on Monday was asked again about his two-way race comments in an appearance on CNN, answering that he was "not going to comment on the other campaigns."

The mayor faced pushback for the comments over the weekend, notably from Sen. Kamala Harris Kamala HarrisTexas Democratic official urges Biden to visit state: 'I thought he had his own plane' The Hill's Campaign Report: Biden on Trump: 'He'll leave' l GOP laywers brush off Trump's election remarks l Obama's endorsements A game theorist's advice to President Trump on filling the Supreme Court seat MORE (D-Calif.), who called the remarks "naive."

"Well, I think ... that it’s naive for him to think that at this point, that the fate of this election has been determined," she said on CBS's "Face the Nation." "Just look at history. You might need to review to know that what’s happening right now is not necessarily determinative of the outcome."

Buttigieg has risen in recent Iowa polls, polling in the top four with Warren, former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE and Sen. Bernie Sanders Bernie SandersSirota reacts to report of harassment, doxing by Harris supporters Republicans not immune to the malady that hobbled Democrats The Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election MORE (I-Vt.).

In addition to gaining traction in polls, Buttigieg has also exchanged jabs with Warren.

Buttigieg knocked Warren's "Medicare for All" plan as a "my way or the highway" approach on Sunday.

“What is just not true is that hers is the only solution. This 'my way or the highway' idea. That either you’re for kicking everybody off their private plans in four years or you’re for business as usual, it’s just not true,” Buttigieg said on ABC’s “This Week.”