The White House continued Tuesday to sow doubt about when and where Americans should be wearing face masks, muddying recommendations from top health officials amid a political back-and-forth between President Donald Trump and his 2020 Democratic rival Joe Biden.

Biden's decision to wear a mask outdoors to a Memorial Day wreath-laying event drew an indirect reply from Trump, who retweeted an image of Biden with a comment, "This might help explain why Trump doesn't like to wear a mask in public." The President has resisted wearing masks in front of cameras.

Trump said on Tuesday during a Rose Garden event that he found Biden's mask "very unusual."

"Biden can wear a mask but he was standing outside with his wife, perfect condition, perfect weather," Trump said, though Biden was standing near others during the memorial. "Inside they don't wear masks and so I thought it was very unusual that he had one on."

The President continued, "But I thought that was fine. I wasn't criticizing him at all. Why would I ever do a thing like that?"

White House press secretary Kayleigh McEnany said during a briefing earlier in the day that it was "peculiar" for the former vice president to don a mask outdoors because he doesn't wear one all the time at home -- though federal guidelines do not recommend masking among people living together.

"It is a bit peculiar, though, that in his basement, right next to his wife, he's not wearing a mask. But he's wearing one outdoors when he's socially distant. So I think that there was a discrepancy there," McEnany said during Tuesday's White House press briefing.

The Centers for Disease Control and Prevention has not recommended Americans wear masks in their homes. Face coverings are recommended in instances where it is impossible to socially distance, and they are now required in many cities when visiting stores or other open businesses.

Biden recently wore a mask for an interview with Stephen Colbert from his home, saying he wears a mask at his house "when anybody's around other than Jill," his wife.

Campaign spokesman Andrew Bates said in a statement after McEnany's comments that Trump had "failed" to provide leadership throughout the pandemic. "Donald Trump's historic disregard for the guidance of public health experts is responsible for a failed response that has led to the deaths of nearly 100,000 Americans and the most devastating job losses our country has suffered since the Great Depression," Bates said.

CNN has asked the White House for clarification on McEnany's comments.

The decision to wear a face mask in public -- already at the center of a national cultural battle over individual responsibility in the pandemic -- emerged as a political wedge this weekend after the two men vying in this year's presidential contest took divergent approaches on Memorial Day.

The unmasked and masked public appearances this weekend by Trump and Biden strengthened the sense that mask wearing has become another issue that divides Americans along ideological and political lines, though many Republicans say wearing a mask in public is wise.

Even Trump's former chief of staff Mick Mulvaney said on Tuesday that mask wearing could help speed an economic revival.

"If we are careful about social distancing and putting on masks and so forth, we should be able to go back to work sooner rather than later," he said in an interview on CNBC.

No White House push for masks

Still, there does not appear to be a growing push at the White House to encourage mask wearing, even though the administration's own public health experts have stressed its importance.

As states begin the process of reopening, masks have appeared on lists of regulations and guidelines for how to safely restart economies and avoid a second outbreak.

That has caused anger among some Americans, who have refused to wear masks and claim the requirement infringes upon their civil liberties. Videos of angry customers refusing to wear masks have gone viral online and the issue has expanded into a debate over the responsibilities of individuals in combating a nationwide crisis.

A clear political divide

Popular opinion is tilted in favor of mask wearing. Sixty-four percent of Americans say everyone should be required to wear masks in public, according to a Quinnipiac poll released last week.

But the same poll showed mask wearing in America has become another political fault line. While 87% of Democrats said masks should be required for everyone in public, 40% of Republicans said the same. And when asked whether Trump himself should wear a face mask when he's in public, 90% of Democrats said he should compared to 38% of Republicans.

The clear political divide hasn't gone unnoticed by the President or his political advisers, nor has the broader cultural debate online that has pitted mask-opposing Trump supporters with those who wear one to further spread.

Trump has so far refused to wear a mask in public, even in places where they are required. Trump did not wear a mask during a trip to a mask production facility in Arizona or a medical equipment and distribution facility in Pennsylvania earlier this month. During a trip to Michigan to visit a Ford plant last week, Trump brought a mask but refused to wear it in front of cameras.

"I didn't want to give the press the pleasure of seeing it," Trump said at the time.

During multiple Memorial Day ceremonies Monday, neither Trump nor Vice President Mike Pence wore a mask -- though the first lady, Melania Trump, was spotted putting on a white mask after boarding Marine One on the White House South Lawn.

White House advisers favor masks

Ahead of the Memorial Day holiday, the White House coronavirus response coordinator Dr. Deborah Birx said there is "clear scientific evidence" that masks work -- adding that she assumes Trump is able to keep six feet of distance "in a majority of cases" when pressed on whether he should wear one.

"What we have said to people is there is clear scientific evidence now, by all the droplet experiments that happened, and that others have done, to show that a mask does prevent droplets from reaching others," Birx said on "Fox News Sunday" when asked what she would tell people who say they have a right not to wear a mask in public.

"Out of respect for each other, as Americans that care for each other, we need to be wearing masks in public when we cannot social distance," she said.

Others close to the administration have also said wearing masks in public could help businesses return to normal.

Mulvaney, who departed his role as acting chief of staff earlier this year, urged the administration to get Americans back to work -- with face masks -- in light of new information on surface spread from the CDC.

"The fact that it's difficult to get this disease from touching stuff, the CDC put out last week, should sort of reset how we look at this," he said during that appearance on CNBC Tuesday when asked how he'd be handling the pandemic if he were still in his old role.

"Much easier to control the projectile coming out of your mouth, the particulate matter, than the stuff that you touch, which you do every single day," he went on. "So if you combine really effective use of masks, which we already should be doing, which is washing our hands and so forth, really, you get a chance to go back now as opposed to waiting around for a vaccine or treatment."

Mulvaney also said he would be "comfortable" in the middle seat of an airplane with the proper PPE.

This story has been updated with details of Tuesday's White House briefing.