State Senate Democrats said a resolute “no” to Gov. M. Jodi Rell’s recent call for a “three-strikes” law when the Senate voted Thursday to approve a new state crime bill and reject an amendment including the governor’s favored provision.

The bill, approved by the Senate, 32-3, would allow a judge to double the duration of a first-time sentence after a second violent crime and triple the sentence after the third crime. The measure, which must still be passed by the House of Representatives, would allow for a life-in-prison sentence on the third offense, state officials said. But a Republican-sponsored third-strike amendment to make the third sentence a mandatory life sentence was rejected, 19-16.

In response, Rell said in a statement that she was disappointed by the weakness of the current bill. And although all Senate Republicans ultimately voted for the bill, many said the bill was too soft. But Democrats who approved the bill said it will ensure tougher sentences.

Yet the three senators who voted in the negative — all from urban Connecticut areas, including New Haven Sen. Toni Harp ARC ’78 — had several concerns about the bill, including a lack of emphasis on urban violent crimes, Senate Democrats Spokesman Derek Slap said.

State Senate Majority Leader Martin Looney said Thursday that the bill will have a “tremendous and tangible influence” on felon sentencing.

“[The bill] sends a very clear message to those criminals who would prey on our state’s citizens,” he said in a press release. “There are really no second chances.”

But Rell said the bill does not have the teeth necessary to ensure adequate sentencing.

Calling the bill little more than “rhetoric … short on effective solutions,” she said in a statement provided by her office that the crime bill would not effectively deter violent criminals from repeating felonies.

“The Senate missed a chance … to put that tougher law on the books,” Rell said.

On Monday, she proposed her own similar crime bill — which included a third-strikes statute — to state officials. But Democrats have largely ignored the bill since then. Some Democrats had introduced an amendment of their own but dropped it during the session when Republicans said they would heavily contest it, Slap said.

Soon after the session ended early Thursday morning, Republicans decried the measure, calling it powerless.

“This amendment pushes us backward,” Sen. John Kissel of Enfield told the Hartford Courant. “How can this be tougher on criminals? It’s not.”

But Brooklyn Sen. Donald Williams, co-chair of the Judiciary Committee, said in a Thursday press conference that the bill would be more effective than a third-strike law because the bill strengthens first- and second-offense penalties.

Still, some Democrats, including Harp, did not vote for the bill. Slap said the three objected to the bill because it is unlikely for state legislators to include funding in next year’s budget for the services provided by the bill. The bill would funnel $10 million into various state departments in order to, among other things, increase probation supervision for sexual offenders and hire more staff for the State Police Major Crime Squad. Slap added that at least one of the dissenting Democrats was troubled that “issues of urban crime haven’t gotten much attention” and the bill does nothing to address the problem.

Slap also said there was a general concern among the three that positive programs — specifically the prisoner-re-entry program — may not be given as much weight by the bill as the harsher sentencing program. But, he acknowledged, the bill does include $10 million for more parole officers and housing for prisoners participating in the program, among other things.

Slap declined to comment further on the concerns and referred comment to the three: Harp, Bridgeport Sen. Edwin Gomes and Bloomfield Sen. Eric Coleman. None of the senators immediately returned requests for comment left on their home phones Thursday night.

The three-strikes law has been the topic of a back-and-forth battle between Democrats and Rell since 2007. Since the legislation originally failed in January 2008, Rell has repeatedly called for the law, citing a need for a change in criminal-justice policy after a July 2007 Chesire home invasion that led to three murders by two men on parole and a March 2008 New Britain home invasion that led to the shooting death of one woman and wounding of another by a career criminal with a laundry-list record of felonies.

Democratic Sens. Joan Hartley of Waterbury, Thomas Gaffey of Meriden and Paul Doyle of Wethersfield all defied party lines and voted to pass the amendment Thursday. All three could not be immediately reached for comment Thursday night.