WASHINGTON — Senators leading the investigation into Russian interference in the November election pledged on Wednesday to conduct an aggressive inquiry, including an examination of any ties to President Trump, as they sought to distance themselves from the flagging efforts in the House.

In a conspicuous show of bipartisanship during a fractious time at the Capitol, the top Republican and Democrat on the Senate Intelligence Committee vowed to forge ahead by interviewing key players connected to Mr. Trump and pressing intelligence agencies to provide all relevant information.

But their display of collegiality seemed intended primarily as a contrast to the explosive and often bewildering statements in recent days from the Republican chairman of the House Intelligence Committee, Representative Devin Nunes of California, whose perceived closeness with the Trump White House has raised doubts about his ability to conduct an impartial investigation.

The chairman of the Senate Intelligence Committee, Richard M. Burr, Republican of North Carolina and a supporter of Mr. Trump during the campaign, suggested on Wednesday that he would not retreat from a process that could damage the reputation of a Republican president.