Following a shooting death during a home invasion in New Britain on Sunday, Gov. M. Jodi Rell has renewed her call for a new “three-strikes” law.

The proposed law would require that offenders convicted of a third violent felony be sentenced to life imprisonment without the possibility of parole.

Republicans in the legislature have supported multiple versions of the bill, but Democrats have argued that such laws limit prosecutorial discretion and lead to a greater number of cases that end in plea bargains, which they say lets violent offenders back onto the streets even earlier.

“We took real steps in January to strengthen our criminal justice systems — but the ghastly crimes in New Britain show us unequivocally that there is more to do and that there are some people who are so evil that ordinary measures will not stop them,” Rell said in a written statement released after the shootings.

Because the three-strikes provisions died in a state legislative committee last Monday, Republican legislators will attach the bill as an amendment to criminal legislation over the next seven weeks before the legislative session ends in order to force debate on the General Assembly floor.

In addition to the three-strikes law, Rell proposed an automatic 50-percent increase in sentence length for anyone convicted of a second sexual offense.

Rell said in her statement that the suspect in Sunday’s shootings — which left a second woman wounded — had a criminal record that included burglaries and a sex offense with a minor.

But Judiciary Committee co-Chair Rep. Michael Lawlor, a Democrat who represents New Haven, said that even under the governor’s current proposal, the previous offenses would not qualify the suspect for punishment under the three-strikes law.

“Under her bill, none of those would have counted as a strike because they were all plea bargained out,” Lawlor said. “That’s what prosecutors do all the time.”

Like a triple homicide in Cheshire that grabbed headlines last summer, Lawlor said, last weekend’s crime is being exploited for political gain because laws that look tough are popular with voters — even if they are not effective at keeping violent criminals off the streets, he said.

Adam Liegeot ’94, a spokesman for the governor, said whether or not this case fit the specifics of the proposed law, the shootings show that much more needs to be done to address persistent violent offenders. The three-strikes law is part of that effort, he said.

“While we may not be comparing apples to apples, what the governor is proposing is a wide range of measures that would address the symptoms of violent behavior that we want to cure,” he said. “The public has written and called the governor en masse, urging her to get measures passed, such as the three-strikes law.”

The bill that died in committee went down by a vote of 25-16.