President Trump on Thursday said he could not definitively say whether he received a COVID-19 test on the day of the first presidential debate, despite a stipulation that both candidates were expected to arrive having tested negative for the virus.

Trump, who tested positive two days after the Sept. 29 debate, insisted during an NBC town hall that he felt physically well during the showdown with Democratic nominee Joe Biden. But he repeatedly hedged when asked whether he had taken a test on the day of the debate.

"I don’t know. I don’t even remember," Trump said when asked directly by NBC's Savannah Guthrie.

"Possibly I did, possibly I didn’t," he said when asked the question again moments later.

White House officials have repeatedly refused to disclose when the president last tested negative prior to testing positive for the virus on Oct. 1. Experts say that information is critical to determining who Trump may have exposed to the virus and whether he might have been infectious at the debate when he was on stage with Biden.

Fox News anchor Chris Wallace, who moderated the first debate, said following the event that Trump did not arrive in time to get tested in Ohio before the event took place.

The president said Thursday he is not tested daily for the virus, but that he is tested "a lot."  

"I was in great shape for the debate, and sometime after the debate I tested positive," he said at Thursday's town hall.

Trump spent three days in the hospital after testing positive for COVID-19 and experiencing fatigue and a fever. He also required supplemental oxygen at times, his physician said.

Despite the severity of his symptoms after his diagnosis, Trump has made a swift return to the campaign trail, holding rallies almost daily.

The president and Biden held dueling town halls on Thursday night in lieu of the second presidential debate. The Commission on Presidential Debates announced the debate would be virtual after Trump's coronavirus diagnosis, but the president refused to participate if the event was not in person. The debate was later canceled.