WASHINGTON — Senate Republicans indicated on Monday that they would not seek to summarily dismiss the impeachment charges against President Trump, proceeding instead to a trial with arguments and the possibility of calling witnesses that could begin as soon as Wednesday.

Dismissal was always a long shot given Republicans’ narrow control of the Senate, but it was the subject of renewed discussion after Mr. Trump said on Sunday that he liked the idea put forward by some conservatives as a way to deny the House’s case the legitimacy of a trial. Other Republicans had signed on to a resolution that would have dismissed the House’s impeachment articles if they were not promptly brought to trial.

In interviews, rank-and-file senators and party leaders made clear on Monday that even if they wanted to pursue dismissal, the votes simply were not there to succeed — at least not at the outset of the trial. They did not rule out considering a motion to dismiss the charges of abuse of power and obstruction of Congress after opening arguments from both sides.

“Our members generally are not interested in a motion to dismiss,” said Senator Roy Blunt of Missouri, a top Republican leader. “They think both sides need to be heard. They believe the president needs to be heard for the first time in a fair setting.”