WASHINGTON — Pressure mounted on Sunday for a broader congressional investigation of Russian cyberattacks aimed at influencing the American election, even as a top aide to President-elect Donald J. Trump said there was no conclusive evidence of foreign interference.

The effort was being led by a bipartisan group of senators, including John McCain, Republican of Arizona, and Chuck Schumer of New York, the Senate Democratic leader, who called on Sunday for the creation of a Senate select committee on cyberactivity to take the investigative lead on Capitol Hill.

“Recent reports of Russian interference in our election should alarm every American,” the senators wrote on Sunday in a letter to Senator Mitch McConnell, Republican of Kentucky and the majority leader, who has said a select committee is not necessary. “Cybersecurity is the ultimate cross-jurisdictional challenge, and we must take a comprehensive approach to meet this challenge effectively.”

The developments served to deepen the fissures between high-ranking lawmakers of both parties who see American intelligence reports implicating Russia as the basis for additional inquiries and Mr. Trump, who continues to reject the conclusions of those reports.