“We believe public officials must set the gold standard for professional behavior, particularly those who hold the high offices of representative, senator, and — especially — president of the United States,” they said in a letter.

Mr. Trump seemed to anticipate the renewed emphasis this week when he declared in a tweet that Democrats, unable to prove campaign collusion with Russia, would resurrect sexual allegations made by women “who I don’t know and/or have never met.”

But in denying any misconduct and attacking Senator Kirsten Gillibrand, Democrat of New York and one of a half-dozen senators who have urged Mr. Trump to resign, the president seemed to only inflame the Democrats and increase calls that he leave office.

The tough Democratic line is a departure from the careful approach that leading Democrats have taken on the subject of impeachment. The majority of House Democrats opposed an attempt last week to initiate impeachment proceedings. Ms. Pelosi and Representative Steny Hoyer of Maryland, the No. 2 Democrat, issued a joint statement pointing to the special counsel looking at the Trump administration and campaign as well as current congressional investigations.

“Those inquiries should be allowed to continue,” their statement said. “Now is not the time to consider articles of impeachment.”

But Ms. Pelosi has strongly endorsed the push for new hearings on the sexual misconduct complaints against the president. “I don’t think that a person who has been a sexual harasser should be president of the United States,” she told CNN.

From a political perspective, the push for hearings over the president’s sexual conduct can serve as a middle-ground alternative to a more polarizing impeachment campaign. It allows Democrats to take aim at a potential vulnerability of the president, who bragged about his groping on a recording, in an environment where little tolerance is being shown for those who are accused, let alone investigated. It can provide some solace to frustrated voters in the Democratic base who don’t think the leadership is being aggressive enough in trying to push Mr. Trump from office. It also forces congressional Republicans and administration officials into the difficult position of either coming up with an explanation for not taking up the allegations or defending the president on a volatile issue.