Gov. Mark Dayton on Tuesday proposed six weeks of paid leave for new parents employed by the state, saying the bonding between newborns and their mothers and fathers “is just crucial.”

More than 35,000 state employees would be eligible for the leave after the birth or adoption of a child — including men — though the governor’s office said that only 500 people are expected to use it annually. The plan would cost taxpayers about $6 million a year.

Dayton described paid leave as key to building a more productive and successful workforce, a crucial issue as his administration has wrestled with how to attract and retain top employees in state government.

He acknowledged that the proposal, which excludes employees in the private sector, was not complete.

“The perfect is the enemy of the very good,” he said. “This is a very big step forward.”

Rep. Sarah Anderson, R-Plymouth, criticized Dayton’s plan for prioritizing public employees over the taxpayers who help pay for the government. As chairwoman of the House State Government Finance Committee, she’s working on legislation that would do more for private-sector employees who want paid time off after having a child.

“I’m trying to find something that everybody can get behind,” said Anderson, who added that she is not ready to release details of her own plan.

Dayton’s package stops short of what DFLers will push in next month’s legislative session. Their plan mirrors laws in California, New Jersey and Rhode Island that require paid family leave for all workers and that extends the benefit to people caring for sick family members. A version of paid family leave failed to win legislative approval in Minnesota last year.

The governor announced the plan during a workforce summit convened by U.S. Labor Secretary Thomas Perez, who traveled to south Minneapolis as part of a national tour to promote paid family and sick leave. It’s also a big topic in the presidential campaigns of Hillary Clinton and Bernie Sanders, who will visit Minnesota later this week and are calling for 12 weeks of paid time off.

Dayton’s announcement caused some confusion at a State Capitol news conference following the summit with Perez, as DFL legislators explained that their initiative was different and more expansive.

Sen. Katie Sieben the architect of last year’s failed initiative, told reporters that Dayton taking the lead on the topic would help her and Rep. Jason Metsa, DFL-Virginia, build the case for “why the rest of the state needs to catch up.”

But, the Newport DFLer said afterward, “They are two different proposals and the two issues really got mixed together.”

By contrast, DFL legislators’ version of paid family leave would be funded through employee payroll contributions. They’re expected to come up with a more detailed plan before the session begins on March 8.

Dayton said he was working with practical limitations. He noted that not only do few states offer more comprehensive paid leave, 13 percent of Minnesotans receive the benefit through their workplaces. Most people, he said, don’t have anything.

The governor said he initially sought four weeks of leave until Lt. Gov. Tina Smith and young mothers on his staff pushed for more. Licensed day care centers in Minnesota already cannot accept infants younger than 6 weeks old, he added.

In 2014, Dayton signed a law extending unpaid leave for pregnant women from six to 12 weeks.

Both proposals face an uncertain fate in the Legislature, where Dayton’s DFL Party controls the Senate and Republicans control the House.

Anderson took a swipe at the political viability of Sieben’s proposal. “When you’re second in command in the Senate and you’ve got a proposal and it doesn’t go through, odds are that there are problems with it,” Anderson said.

The Mayo Clinic, U.S. Bank, Target, Ecolab and General Mills are among the major private employers that offer paid family leave, according to the governor’s office. Hennepin County, the cities of Minneapolis and St. Paul, the University of Minnesota, and the Minnesota State Colleges and Universities system also have adopted the policy.

Laws haven’t caught up with the changing face of America, Perez told a crowd of DFLers and labor advocates after Dayton spoke at the Rev. Dr. Martin Luther King Jr. Recreation Center.

“More dual career couples working, that’s a good thing,” Perez said. “But at the same time, our laws didn’t evolve. We’re in the ‘Modern Family’ universe, but we have ‘Leave it to Beaver’ policies on paid leave and child care.”

Maya Rao • 651-925-5043