ST. PAUL — Gov. Mark Dayton and legislative leaders on Friday penciled in a special session for late August to revive a tax bill and hundreds of millions of dollars in public construction projects, but it’s not a done deal yet.

Minnesota’s top politicians have struggled to hammer out the terms of an overtime session since the Legislature adjourned in late May, leaving a $1 billion-plus public works package unfinished. Dayton added to the pile by vetoing a $260 million tax relief package, citing a wording error.

After on-and-off meetings yielded little progress for weeks, Dayton and the leaders from the Republican-controlled House and Democrat-majority Senate emerged from their latest private session Friday with a goal of calling lawmakers back to St. Paul in the third week of August. But in order to make that happen, they need to address lingering disagreements on the final size of the public construction bill and whether it will include funding for a light-rail train to Minneapolis suburbs — a project Republicans dislike.

“Where there’s a will, there’s a way. The will is there, I believe, to work these final details out,” Dayton said.

Republican House Speaker Kurt Daudt said negotiators have agreed to approve again the Legislature’s tax bill with few changes, aside from fixing a typo that prompted Dayton’s veto and restoring some funding for the state’s high school league. That bill would offer tax credits for college graduates with loan debt, tax cuts for working families and a property tax exemption for the planned Major League Soccer stadium in St. Paul.

In the days after he declined to sign that bill, Dayton told lawmakers he wouldn’t call a special session unless the Legislature kicked in extra money for Minnesota’s public colleges and universities and restore funding for some business subsidy programs. Facing slim odds of Republicans agreeing to more spending, Dayton said Friday he’d drop those requests.

But the final size of the so-called bonding bill — and what construction projects would be included — remains to be seen. The governor said he’s pushing to ensure it includes funding for renovations at the state’s security hospital and other facilities. But Daudt said he and GOP lawmakers hope to keep the final price tag under $1 billion, noting that some additional projects could be covered with cash or other funds.

Long a divisive issue at the Capitol, state funding for the proposed light-rail train between Minneapolis and the suburbs is still a sticking point. Before lawmakers start meeting next week to iron out those final details, Democratic Senate Majority Leader Tom Bakk said he was confident they could line up an alternate funding source that would help unleash federal funding for the project.

“I think that we’re going to find some resolution on that,” he said.