WASHINGTON — President-elect Donald J. Trump said on Sunday that he had fallen short in the popular vote in the general election only because millions of people had voted illegally, leveling the baseless claim as part of a daylong storm of Twitter posts voicing anger about a three-state recount push.“In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally,” Mr. Trump wrote Sunday afternoon.The series of posts came one day after Hillary Clinton’s campaign said it would participate in a recount effort being undertaken in Wisconsin, and potentially in similar pushes in Michigan and Pennsylvania, by Jill Stein, who was the Green Party candidate. Mr. Trump’s statements revived claims he made during the campaign, as polls suggested he was losing to Mrs. Clinton, about a rigged and corrupt system.The Twitter outburst also came as Mr. Trump is laboring to fill crucial positions in his cabinet, with his advisers enmeshed in a rift over whom he should select as secretary of state. On Sunday morning, Kellyanne Conway, a top adviser, extended a public campaign to undermine one contender, Mitt Romney — a remarkable display by a member of a president-elect’s team. In television appearances, she accused Mr. Romney of having gone “out of his way to hurt” Mr. Trump during the Republican primary contests.Claims of wide-scale voter fraud have been advanced for years by Republicans, though virtually no evidence of such improprieties has been discovered — especially on the scale of “millions” that Mr. Trump claimed.Late on Sunday, again without providing evidence, he referred in a Twitter post to “serious voter fraud in Virginia, New Hampshire and California.”A day earlier, Mr. Trump’s transition team ridiculed the idea that recounts were needed. “This is a scam by the Green Party for an election that has already been conceded,” it said in a statement, “and the results of this election should be respected instead of being challenged and abused.”That message runs counter to the one Mr. Trump sent on Sunday with his fraud claims — if millions of people voted illegally, presumably officials across the country would want to pursue large-scale ballot recounts and fraud investigations.But the Twitter posts could energize some of his supporters, who have claimed online that Mrs. Clinton’s two million-vote lead in the popular vote has been faked. Mr. Trump at times promoted other conspiracy theories during the campaign, including claiming that Senator Ted Cruz’s father was somehow tied to the assassination of President John F. Kennedy.Many of Mrs. Clinton’s supporters have been galvanized by the notion that vote recounts in the three states — where Mr. Trump leads by a combined total of about 100,000 votes — could somehow overturn Mr. Trump’s commanding Electoral College victory. By announcing, three weeks after Mrs. Clinton conceded the race, that it would participate in the Wisconsin recount, her team has helped reignite the contentious atmosphere of the campaign, of which Mr. Trump’s Twitter barrages were a fixture. (By all accounts, Mr. Trump types out his Twitter posts himself on his phone.)After spending almost five days in Palm Beach, Fla., where he celebrated Thanksgiving at his Mar-a-Lago resort, Mr. Trump made no public statements on Sunday other than those via Twitter. He returned in the afternoon to Trump Tower in Manhattan.Through the day, Mr. Trump appeared fixated on the recount and his electoral performance. In a series of midafternoon Twitter posts, not long before he boarded his flight, Mr. Trump boasted that he could have easily won the “so-called popular vote” if he had campaigned only in “3 or 4” states, presumably populous ones.“I would have won even more easily and convincingly (but smaller states are forgotten)!” he wrote.The afternoon messages followed a string of early-morning Twitter posts in which the president-elect railed against the recount efforts. In an initial post at 7:19, Mr. Trump wrote: “Hillary Clinton conceded the election when she called me just prior to the victory speech and after the results were in. Nothing will change.”He went on to quote a comment by Mrs. Clinton during one of their debates, in which she said she was horrified by Mr. Trump’s refusal to say that he would accept the outcome of the election. And he noted that in her concession speech, she had urged people to respect the vote results.“‘We have to accept the results and look to the future, Donald Trump is going to be our President,’” Mr. Trump wrote on Twitter, quoting Mrs. Clinton. “‘We owe him an open mind and the chance to lead.’ So much time and money will be spent — same result! Sad.”One person who spoke with Mr. Trump over the holiday weekend said the president-elect had appeared to be preoccupied by suggestions that a recount might be started, even as his aides played down any concerns. Another friend said Mr. Trump felt crossed by Mrs.