Doug Jones, the Democrat who won a shock victory in the Alabama Senate election, said on Sunday he did not think Donald Trump should resign as president in light of sexual misconduct allegations against him.

It was time, Jones said, to “get on with the real issues that are facing the people of this country right now”.

Multiple women have accused Trump of sexual misconduct. The president, who was recorded saying he could “grab” women “by the pussy”, denies all such allegations. The White House has said all the women are lying.

Last weekend, however, cabinet member Nikki Haley said the women who have accused Trump “should be heard”. A group of Trump accusers subsequently called for a congressional investigation and a group of Democratic senators led by Kirsten Gillibrand of New York called for Trump to resign.

Appearing on CNN’s State of the Union on Sunday, Jones was asked if he would join new Senate colleagues including Cory Booker of New Jersey, who campaigned for him, in calling for the president to resign.

He said: “Where I am on that right now is that those allegations were made before the election. And so people had an opportunity to judge before that election. I think we need to move on and not get distracted by those issues.

“Let’s get on with the real issues that are facing people of this country right now, and I don’t think the president ought to resign at this point. We’ll see how things go but certainly those allegations are not new and he was elected with those allegations at front centre.”

Jones echoed White House press secretary Sarah Huckabee Sanders, who told reporters on Monday: “The people of this country, at a decisive election, supported President Trump, and we feel like these allegations have been answered through that process.”

Trump said before his election victory over Hillary Clinton that he would sue all his accusers after the election. That has not happened and more accusers have come forward.

Since the downfall of the Hollywood producer Harvey Weinstein over multiple allegations including sexual assault and rape, which he denies, a number of powerful men have been the subject of allegations of sexual misconduct.

On Saturday a third congressional Democrat, Ruben Kihuen of Nevada, announced he would quit Congress over allegations of inappropriate sexual behaviour. Two Republicans, Trent Franks and Blake Farenthold, have also announced the end of their congressional careers.

On CNN, Jones was asked why Al Franken, the Democratic senator from Minnesota who announced his resignation over accusations of sexual misconduct, should have to resign over offences allegedly committed before he was elected if Trump did not.

Jones said: “Again, I go back to the fact that those allegations were made and he was elected president of the United States and I think the American people have spoken on that at this time.

“There’s other things out there but I think at this point we need to move on and try to work with some real issues that are facing the country and not worry about getting at odds with the president any more than we have to.”

Jones, who also appeared on Fox News Sunday, was asked about his opponent Roy Moore’s refusal to concede the Alabama election. “I think it’s time to move on,” he said, adding that Moore was “hurting the people of Alabama”.