President Trump’s commission investigating voter fraud held its first meeting Wednesday amid a swirl of partisan acrimony and questions about whether it is looking for facts or has already decided which facts it is trying to find.

The session featured an early statement by Mr. Trump, whose baseless claim that he would have won the popular vote in 2016 if not for millions of illegal voters hung over the gathering. He said he was told stories during and after his presidential campaign of voting irregularities “in some cases having to do with large numbers of people in certain states.”

The meeting’s coda was an MSNBC television interview in which Kris Kobach, the Kansas Republican who is the panel’s vice chairman and de facto head, was asked, “Do you believe Hillary Clinton won the popular vote by three to five million votes because of voter fraud?” He replied: “We will probably never know the answer to that question. Because even if you could prove that a certain number of votes were cast by ineligible voters, for example, you wouldn’t know how they voted.”

Mr. Kobach, one of the nation’s leading advocates of tougher voting restrictions, later said that he was addressing whether the exact breakdown of legal votes could be known, not who won, and that similar doubts hung over tallies in states that Mr. Trump won.