AUGUSTA, Maine — The Legislature’s two top Democratic leaders met with Gov. Paul LePage on Monday, two months after LePage called off previously scheduled meetings with them, upset that the Maine Democratic Party had dispatched a tracker to film him at public events.

House Speaker Mark Eves of North Berwick and Senate President Justin Alfond of Portland had tried to schedule a meeting with the Republican governor soon after their party recaptured control of both chambers of the Legislature following November’s elections. LePage, however, said he wouldn’t meet with them until they called on their party to stop filming him at public events.

Eves and Alfond met Monday with LePage, along with House Republican leader Ken Fredette of Newport and Senate Republican leader Michael Thibodeau of Winterport, said Jodi Quintero, Eves’ spokeswoman. The meeting, held in the governor’s Cabinet room, lasted about an hour, she said.

“It was great to finally meet with the governor, and the speaker was pleased with the meeting,” Quintero said. “We look forward to working together. The challenges we face are too big for one party to solve alone.”

Quintero said the meeting touched on a “range of issues,” including LePage’s budget proposal, energy, education and workforce development. Eves went into the meeting hopeful that Democratic leadership could establish regular lines of communication with the chief executive.

“We have to work together,” Quintero said. “The speaker is very serious about working together, finding common ground where possible, because we have no other choice.”

Fredette said Monday’s meeting was productive and that more will likely follow.

“Establishing working relationships between the principal players is an important part of having a smoothly operating state government,” he said.

Adrienne Bennett, a spokeswoman for LePage, said the governor “thought it was a pleasant conversation.”

Monday’s meeting took place nearly three weeks after LePage met with another group of lawmakers, three independent House members who aren’t caucusing with either the chamber’s Democrats or Republicans. According to those lawmakers, LePage swore, stormed out of the meeting, and pounded the table after the legislators — Reps. Joe Brooks of Winterport, Jeff Evangelos of Friendship and Ben Chipman of Portland — questioned a proposal in LePage’s two-year budget package to suspend revenue sharing with municipalities.

Just days after news of that meeting became public, Fitch Ratings downgraded Maine’s general obligation bond debt a notch, to “AA” from “AA-plus.” Among the reasons Fitch cited was “an increasingly contentious decision-making environment” after Democrats reclaimed control of the Legislature. The split-party control, Fitch said, raised “the likelihood of increased conflict with the Republican governor over the supplemental budget and the biennial budget.”