After meeting with DFL legislative leaders, Gov. Mark Dayton on Monday said he and Senate DFLers will push for a larger increase on the basic school funding formula, an overall 4 percent increase than current Dayton and Senate proposals calling for a 2 percent increase.

Aid dollars from the state form the basis of most school district budgets. Some DFL lawmakers have complained 1 percent a year would not be sufficient for a number of districts facing budget deficits, and Dayton said after a private meeting with a handful of top DFL lawmakers that they now want to double that.

“The Senate and I agree that 2 percent … for each of the next two years is the minimum of what’s necessary,” Dayton told reporters. How to pay for it though is still unclear. “All this stuff is fluid at this point,” he said.

In the education funding bill approved by the GOP-led House, the per-year increase are a half-percent each year.

Dayton also added that he is not surrendering on his other high-profile education priority, a funding boost of about $350 million aimed at helping every public school statewide offer preschool classes for 4-year-olds.

While Dayton characterized the 2-and-2 aid boost as agreed upon between himself and DFL senators, Majority Leader Tom Bakk left some doubt.

“I’m not suggesting it,” said Bakk, DFL-Cook. He said Dayton brought up the 2-and-2 proposal during Monday’s meeting, but did not indicate where else in the budget that money could be shifted to cover that kind of spending.

GOP Rep. Jennifer Loon, who sponsored the House education bill, said it would be difficult to provide an aid boost of that size while also delivering on Dayton’s preschool initiative.

“I’d love to do it, but we have to get the budget to balance with the resources available,” said Loon, of Eden Prairie.