Connecticut Democrats and Republicans released competing proposals Tuesday on how to curb gun violence following the deadly shooting in December at Sandy Hook Elementary School.

Democrats proposed a broader agenda that included an expansion of the state's bans on assault-style weapons and ammunition magazines with more than 10 bullets. Those were the two most politically charged ideas, and the Republicans wouldn't sign on to them.

Democrats also want to require permits for people to buy rifles or shotguns—they are now required for handgun purchases—and tougher so-called suitability standards to carry pistols and revolvers.

Republicans proposed increasing to 21 the minimum age to buy rifles that accept magazines with more than 10 rounds.

Authorities have said Sandy Hook shooter Adam Lanza used an AR-15 assault-style rifle with a 30-round magazine to kill his 27 victims in Newtown, Conn. Both would be illegal under the Democratic proposal.

"We are New Englanders, change doesn't come easy," said Rep. Craig Miner, the Republican co-chairman of a legislative task force on gun control. He made the remarks Tuesday during the group's final public meeting.

Mr. Miner said the task force's eight Democrats and eight Republicans didn't agree on every proposal but said "we do have broad consensus on many things."

Both parties called for background checks on all gun purchases, the establishment of a statewide deadly-weapon offender registry and stiffer penalties on gun trafficking. Democrats and Republicans are also calling for stricter gun-storage laws and requiring permits of gun shows.

Some of the task-force members expressed concern about the group's failure to come up with a list of consensus proposals. "I don't think we will have fulfilled our mission if we just pass along two lists," said state Sen. John Kissel, a Republican.

"I disagree," said State Sen. Martin Looney, the task force's Democratic co-chairman, in response to Mr. Kissel. "I think we have met the charge in what we need to do…I think it's quite clear that we have consensus on some items and not on others."

These proposals now go to six legislative leaders—four Democrats and two Republicans—tasked with hashing out a bill expected to include measures on gun control, school safety and mental health. Democrats control the state House of Representatives and the Senate.

"All six of us will have a vigorous discussion from here on," said Mr. Looney, who is also the Senate Majority Leader.Andrew Doba, a spokesman for Democratic Gov. Dannel Malloy, said, "It's encouraging to see that there is much common ground between their work and the proposals outlined by the governor.As the governor said, the time to act is now. We hope they move quickly toward resolution."

The mental-health task force also issued proposals Tuesday. It called for more training for teachers, school nurses and counselors to identify mental illness; a mental-health task force to study how to improve the system for young people; and more resources for case management for people with mental illnesses.