ALBANY – In a state that for generations has protected abortion rights, lawmakers in both houses Thursday wrangled over whether to create additional protections in the event federal abortion rights laws are ever eliminated.

Despite threats of political retaliation by both Gov. Andrew M. Cuomo and women’s organizations, leaders of the State Senate say they will not let a bill come to a vote that backers say will codify state law to protect abortion rights in case the Roe v. Wade decision is ever overturned.

Supporters say the measure is needed because abortion rights continue to be at risk, and they point to a new effort in the House of Representatives as the most recent proof.

But critics say the governor and his supporters are trying to score political points out of a non-issue and note the Supreme Court has not reversed Roe v. Wade despite legal challenges, even when the court was dominated by conservative justices.

The Assembly on Thursday spent nearly four hours debating, and then passing, a 10-point package addressing various women’s issues, including strengthening sexual harassment and human-trafficking laws. But it was the 10th point – abortion rights – that dominated the debate.

“The Assembly had the courage to stand up on behalf of the women of New York, and now the Senate must do the same,’’ Cuomo said.

The package of bills comes just weeks after the resignation of Vito Lopez, a former powerful Brooklyn Democratic Assembly member who was accused of sexually harassing and groping young female staff members. The incident was a blow to Assembly Speaker Sheldon Silver, who approved a secret, taxpayer-funded settlement with two of the women. After Thursday’s vote, Silver, who beat back calls from critics for his resignation, was feted at a news conference by female lawmakers and advocates for passing the bill.

Cuomo has loudly pushed the issue, calling it a “litmus test” for state senators if the matter is not brought to a vote today. He said residents deserve to know whether their representatives in Albany oppose or support abortion rights.

While Cuomo has called his measure “historic,” he also has acknowledged that it has no immediate practical impact. Critics, though, say the measure encourages abortions and could expand late-term abortions, a claim advocates strongly dispute.

“To me, no legislator or attorney can alter the law to make morality right and morality wrong … An innocent life should never be taken,” Assemblyman David DiPietro, an Erie County Republican, said during the floor debate, choking up as he spoke.

But the real fight and lobbying have been in the State Senate, and the matter digs far deeper than the proposed legislation. In forming their coalition government, Senate Republicans and four breakaway Democrats agreed that no bill would reach the floor for a full chamber vote unless Senate co-leaders Dean Skelos, a Long Island Republican, and Jeff Klein, a Bronx Democrat, agree.

Skelos, whose GOP colleagues already are taking a political hit from conservatives after letting a sweeping gun-control law be approved in January, is adamant that the abortion bill will not reach the floor.

Kelly Cummings, a spokeswoman for Skelos, said the State Senate today expects to take up a nine-point “women’s equality” package of bills proposed by Cuomo.

“Senator Skelos continues to oppose bringing the governor’s abortion provision to the floor,’’ she said.

For Skelos and Klein, a violation of their agreement on how bills reach the floor would drive a stake into the coalition deal that has held tight the past six months. And Skelos has made clear to important political forces, including religious groups and the state Conservative Party, that Cuomo’s abortion bill is dead.

In the unusual deal they struck to share power, Klein and Skelos switch the title of majority leader each day of the legislative session; today, it will be Klein’s turn. Legislative sources say they expect a procedural maneuver by Senate supporters to try to force a floor vote.

But critics, who don’t believe the plan has enough votes anyway, remain confident Skelos will prevail. If not, they say, he could face serious internal party troubles.

“I am very comfortable that it will not come to the floor,” said Conservative Party Chairman Michael Long.

If Klein and his three breakaway Democratic colleagues were to surprise Albany and push the bill to the floor, Long said, they would be betraying the agreement on how the Senate is being run.

Klein this week said he and his fellow independent Democrats are prepared to adopt nine of the 10 points in the women’s agenda package. But he said “the votes are just not there” in the Senate to pass the abortion bill.

The four Democrats are all abortion-rights advocates, and women’s groups were putting intense pressure on them Thursday to get the bill to the floor.

“No more excuses … There has to be time for women, and the time is now,” said Andrea Miller, president of NARAL Pro-Choice New York.

The Assembly did not pass a Cuomo plan to break the 10 issues into 10 separate bills; lawmakers said the 10 separate pieces contained weakened provisions from the comprehensive measure. The Senate could take up the 10 separate versions, making the whole exercise symbolic unless the Assembly then took the matching bills up today.

New York legalized abortion in 1970.

“Since we live in a democracy, and majority rules, a woman should have a right to choose,” said Assemblywoman Crystal Peoples-Stokes, a Buffalo Democrat.

But one lawmaker called the debate “theatrics” because critical women’s rights issues, such as new sexual harassment protections, are in jeopardy because the State Senate and Assembly versions do not match as a result of the different approaches to the abortion provision.