ST. PAUL — Gov. Mark Dayton on Thursday opened the door for a transportation funding package without a gasoline tax hike, a sign that Republican legislative leaders hoped would pave the way to finally approving new money for road and bridge repairs after years of failed efforts.

Dayton and lawmakers have struggled to pass a major road and bridge funding package amid partisan divides over how to pay for it. Dayton and Democrats have pushed for a gas tax hike, while Republicans have insisted the budget surplus and existing tax revenues are sufficient.

Although Dayton still stressed he believes a 10-cent gas tax bump is the best route and cautioned that he’ll safeguard government programs that could lose out on money rerouted to transportation funds, he’s outnumbered by Republicans who now control both the House and Senate. The governor said he wouldn’t veto a bill that repurposes existing general fund dollars and doesn’t include a gas tax.

“An inadequate bill is better than no bill,” he said.

Republicans and Democrats alike have made funding a backlog of unfunded construction needs across the state a top priority for years. If passed this year, it would be the first major boost for road and bridge funding since 2008.

The GOP-controlled House and Senate have approved funding packages that relies on borrowing, tapping part of a healthy budget surplus and shifting $400 million-plus in existing taxes on car parts, rentals and leases from the state’s general fund to its dedicated transportation fund.

Republican House Speaker Kurt Daudt called Dayton’s softening opposition a “huge step” as the Legislature works to finalize a new, two-year budget in the next month.

“Transportation is the place where I’m probably most optimistic,” Daudt said.

The debate over road and bridge repairs — and how much of the state’s existing taxes should be repurposed for them — will play a pivotal role in the broader budget negotiations. Senate Majority Leader Paul Gazelka said he hopes to wrap up a deal on transportation early on to ease the rest of the work.

But there are still lingering issues that could make it tricky, like Republican opposition to funding mass transit projects and Democratic concerns that the proposed GOP budget cuts to the Metropolitan Council, which runs light rail routes, could harm bus service.

Gazelka said the two sides are close to an agreement, including boosting funding for bus transit.