Mr. Trump had been resisting any move toward a transition. But in conversations in recent days that intensified Monday morning, top aides — including Mark Meadows, the White House chief of staff; Pat A. Cipollone, the White House counsel; and Jay Sekulow, the president’s personal lawyer — told the president the transition needed to begin. He did not need to say the word “concede,” they told him, according to multiple people briefed on the discussions.

Mr. Trump continued to solicit opinions from associates, including Rudolph W. Giuliani, who told him there were still legal avenues to pursue, the people said.

Some of the advisers drafted a statement for the president to issue. In the end, Mr. Trump did not put one out, but aides said the tone was similar to his tweets in the evening, in which he appeared to take credit for Ms. Murphy’s decision to allow the transition to begin.