WASHINGTON — Senator Al Franken, back at the Capitol for the first time since groping accusations emerged nearly two weeks ago, gave no indication on Monday that his political career was in peril, telling reporters that he would work to try to regain the trust of women, voters and his colleagues.

“I know there are no magic words that I can say to regain your trust,” Mr. Franken, a Minnesota Democrat, said during a brief and contrite news conference outside his Senate office. “I know that it’s going to take time.”

Mr. Franken, 66, has been fighting for his political life in the face of accusations of improprieties from four women. Capitol Hill has been dominated in recent weeks by allegations of sexual impropriety and how to address them, but so far, Mr. Franken is the only senator under scrutiny.

His fellow senators have largely been unwilling to extend Mr. Franken lines of support, and on Sunday, one of them, Marco Rubio, Republican of Florida, said Mr. Franken ought to consider resigning.