Nonetheless, Mr. Trump said he still hoped Democrats will work with him on bipartisan legislation in the coming year to overhaul health care, improve the country’s crumbling infrastructure and help young immigrants brought to the country as children.

Mr. Trump disputed reports that suggested he does not have a detailed understanding of legislation, saying, “I know the details of taxes better than anybody. Better than the greatest C.P.A. I know the details of health care better than most, better than most.”

Later, he added that he knows more about “the big bills” debated in the Congress “than any president that’s ever been in office.”

The president also spoke at length about the special election this month in Alabama, where Roy S. Moore, the Republican candidate, lost to a Democrat after being accused of sexual misconduct with young girls, including a minor, when he was in his 30s.

Mr. Trump said that he supported Mr. Moore’s opponent in the Republican primary race because he knew Mr. Moore would lose in the general election. And he insisted that he endorsed Mr. Moore later only because “I feel that I have to endorse Republicans as the head of the party.”

Mr. Mueller’s investigation appears to be moving ahead despite predictions by Mr. Trump’s lawyers this year that it would be over by Thanksgiving. Mr. Trump said that he was not bothered by the fact that he does not know when it will be completed because he has nothing to hide.

Mr. Trump repeated his assertion that Democrats invented the Russia allegations “as a hoax, as a ruse, as an excuse for losing an election.” He said that “everybody knows” his associates did not collude with the Russians, even as he insisted that the “real stories” are about Democrats who worked with Russians during the 2016 campaign.