It remains to be seen whether Mr. Trump’s stated doubts about Russia’s involvement will subside after Monday’s Electoral College vote. He and his allies have been concerned that the reports of Russian hacking have been intended to peel away votes from him, although even Democrats have not gone so far as to say the election was illegitimate.

“Right now, certain elements of the media, certain elements of the intelligence community and certain politicians are really doing the work of the Russians — they’re creating this uncertainty over the election,” Representative Peter T. King, Republican of New York, told reporters on Thursday after meeting with Mr. Trump.

But many other Republicans, including Senator Mitch McConnell of Kentucky, the majority leader, and Senator John McCain of Arizona, have publicly argued that the evidence leads straight to Russia. They have called for a full investigation, and Senator Dianne Feinstein, Democrat of California, who sits on the Senate Intelligence Committee, urged Mr. Obama on Thursday to complete an administration review quickly.

Mr. Trump’s Twitter post was his latest move to accuse the intelligence agencies he will soon control of acting with a political agenda and to dispute the well-documented conclusion that Moscow carried out a meticulously planned series of attacks and releases of information to interfere in the presidential race.

But as he repeated his doubts, Mr. Trump seized on emerging questions about the Obama administration’s response: Why did it take months after the breaches had been discovered for the administration to name Moscow publicly as the culprit? And why did Mr. Obama initially opt not to openly retaliate, through sanctions or other measures?