Top Democratic officials on Tuesday reiterated their support for an independent investigation of sexual harassment allegations against New York Gov. Andrew M. Cuomo — some saying the accounts are “troubling” — but did not join increasing calls for the embattled governor to resign.

Three women — two who worked for Cuomo (D) and another who described an encounter with him at a 2019 wedding — have accused the governor of inappropriate comments or unwanted touching.

In a statement Sunday, Cuomo said he “never intended to offend anyone or cause any harm” and described his actions as a result of his “playful” nature, but denied inappropriately touching anyone.

New York Attorney General Letitia James is launching an investigation of the claims, which will be led by an outside law firm — a move endorsed by senior congressional leaders.

Senate Majority Leader Charles E. Schumer (D-N.Y.) on Tuesday called the accusations “serious, very troubling” and said he trusted the New York attorney general to conduct a thorough and apolitical investigation.

“These women have to be listened to,” Schumer told reporters on Capitol Hill. “I always believed that sexual harassment is not acceptable, must not be tolerated.”

House Speaker Nancy Pelosi (D-Calif.) and Rep. Hakeem Jeffries (N.Y.), chairman of the House Democratic Caucus, took a similar stance.

“These allegations are very serious against Governor Cuomo, made by serious individuals and deserve a serious and independent investigation,” Jeffries said.

New York political operatives and aides said Schumer — no personal fan of the governor — and other senior Democrats were unlikely to call for Cuomo’s resignation unless more damaging accusations come out. And the governor currently has no plans to resign unless he faces significantly more pressure to do so, with his office on tenterhooks to see if more women come forward, according to people who spoke on the condition of anonymity to describe internal conversations.

Cuomo has survived other scandals, advisers noted, including the conviction of his top aide on corruption charges and Cuomo’s premature closing of an anti-corruption commission — a move that sparked a federal investigation.

So far, just one House Democrat, Rep. Kathleen Rice (N.Y.), has called for Cuomo to step down, joining an assortment of state lawmakers and groups on the left such as New York’s Working Families Party and UltraViolet, a national women’s advocacy group.

If there are mounting calls for Cuomo to leave office, that could ramp up the pressure on Democrats, who opposed Supreme Court Justice Brett M. Kavanaugh’s nomination after Christine Blasey Ford accused him of assaulting her when they were in high school.

Sen. Kirsten Gillibrand (D-N.Y.), who made issues of sexual assault and violence against women a cornerstone of her short-lived presidential campaign, echoed her support for an independent investigation Tuesday.

“The women who have come forward have shown tremendous courage and must be treated with respect and dignity,” she said in a statement. “The behavior described in these allegations against Governor Cuomo is completely unacceptable.”

Rep. Carolyn B. Maloney (D-N.Y.), who has been a lead sponsor of legislation to combat sexual harassment in the workplace, told reporters on Capitol Hill, “I believe women, so I think it should be thoroughly investigated.”

At the White House, press secretary Jen Psaki said Tuesday that President Biden and Vice President Harris “both believe that every woman coming forward should be heard, should be treated with dignity and treated with respect.”

Several people close to Cuomo described the current moment as the nadir of his long political career but said that they believed he could still survive if no other allegations emerge.

Behind the scenes, the governor and his allies have so far been successful in urging lawmakers and other politically influential figures in New York to hold off on resignation calls, two advisers said.

Cuomo’s office declined to comment.

Some allies were pushing the governor and his team to hold a public event in the upcoming days to shake off the perception that the controversy has become all-consuming. “The only way he survives is that if the allegations stop coming in and he can show he is actually governing,” said one person who regularly speaks to Cuomo, who, like others, spoke on the condition of anonymity to describe private conversations. “He just has to slow things down.”

The people described an office besieged by the harassment allegations and an inquiry into how he handled nursing homes during the pandemic — and a livid governor.

Cuomo aides were caught off guard by the third accusation, made Monday by Anna Ruch, who described the governor putting his hand on her bare back and grabbing her face at a 2019 wedding attended by many of his top staffers.

Amid the controversies, Cuomo has been left without prominent public defenders, a product in part of his fraught relationship with other Democrats. The governor is known for volcanic eruptions and an aloof personality that have alienated even some of his allies, several advisers acknowledged.

He has a particularly contentious relationship with New York Mayor Bill de Blasio, who in the wake of the allegations has called for Cuomo to be stripped of his gubernatorial emergency powers while under investigation. Rice, the House lawmaker who called for his resignation, battled with Cuomo over his premature shuttering of the anti-corruption commission.

Still, Cuomo is a fixture in Democratic politics, the son of a popular former New York governor and a Cabinet secretary in President Bill Clinton’s administration. He has deep ties to city and state labor unions and a formidable record on Democratic issues.

“They’d all like to kill him,” said Hank Sheinkopf, a political consultant who has worked for Cuomo in the past. “But the problem is, if you take a shot at the king, you better actually kill him.”

The pressure on Cuomo so far is coming mostly from the left. The New York Working Families Party, a liberal party that has had influence in the state’s elections, called on Cuomo to resign Tuesday. The party has a contentious history with Cuomo and backed “Sex and the City” actress Cynthia Nixon against him in the 2018 gubernatorial primary.

“Andrew M. Cuomo’s reign of fear, harassment and intimidation cannot continue,” said the party’s state director, Sochie Nnaemeka. “We were horrified to learn of the Governor’s pattern of sexual harassment. We have been equally disturbed by the Governor’s response: He did not deny any of Charlotte Bennett’s specific allegations, failed to take any personal responsibility for his actions and instead blamed his victims.”

Bennett, a former Cuomo aide, alleges that the governor asked her intrusive personal questions, which she interpreted as sexual advances.

Also Tuesday, six Democratic Socialist state legislators called for Cuomo’s impeachment for abuses of power, citing the sexual harassment allegations as well as accusations that he covered up the extent of the coronavirus crisis in New York nursing homes.

“Governor Cuomo has repeatedly abused his powers and yet has faced no accountability,” the lawmakers said in a statement. “We must utilize every mechanism to lead a process commensurate with the severity of the governor’s multiple abuses of power.”

Others stopped short of calling for his ouster.

Erinn Robinson, a spokeswoman for the Rape, Abuse & Incest National Network (RAINN), said in a statement that “the allegations against Gov. Cuomo are deeply troubling and deserve careful investigation, and we urge Gov. Cuomo to cooperate fully. Anyone who has behaved in the manner alleged does not belong in a position of leadership.”

Seung Min Kim contributed to this report.