While it may have been cold outside, Portland Mayor Ethan Strimling was busy trying to thaw the city’s icy relationship with Gov. Paul LePage over a lunch of steak and potatoes at the Blaine House on Tuesday.

Strimling said the 2 1/2-hour meeting with the governor didn’t lead to any deals or joint policy initiatives, but marked a significant step toward restoring the relationship between Augusta and the state’s economic center that had grown increasingly strained under the former mayor, Michael Brennan.

“It was a pretty free-flowing conversation,” Strimling said, noting they debated issues like tax policy, local control and ways to move people out of poverty. “I hope we’re able to continue the conversation and build a relationship where we can agree to disagree.”

Strimling said he gave the governor a bottle of red wine – Cabernet Sauvignon – and that the two exchanged cellphone numbers.

Although LePage has been critical of Portland’s welfare spending, his spokeswoman, Adrienne Bennett, said the governor is willing to discuss serious ideas for good public policy.

“While on opposite sides of the political aisle, the governor and Mayor Strimling have maintained a positive working relationship through the years and that’s because it’s not about a photo op or headline,” Bennett said. “Instead, they are two people making an honest effort to identify common ground on how to achieve similar goals.”

Strimling unseated Brennan as Portland’s mayor in November. Brennan was eager to engage LePage in political battles, often highlighting his clashes throughout the campaign, whether it was defending the city’s social services programs from criticism or fighting budget proposals that would negatively impact the city.

LePage also falsely described Portland as a “sanctuary city,” where local officials don’t assist federal authorities in the deportation of illegal immigrants, and said in a handwritten note to a Cape Elizabeth librarian that residents in southern Maine “ignored and welcomed” corruption.

Strimling has taken a more conciliatory approach to LePage, saying that he would sit down and talk to anyone interested in the future of Portland, including the governor. As director of LearningWorks, a Portland nonprofit that helps low-income families, at-risk kids and immigrants, Strimling established a good working relationship with LePage, who overcame poverty and abuse as a child.

That relationship nearly prompted LePage to endorse Strimling over Brennan during two separate radio interviews. As the mayoral campaign entered its final weeks, Brennan tried unsuccessfully to turn that relationship into a liability.

Strimling won with 51 percent of the vote in a three-way race.

Shortly after the November election, Strimling and LePage met briefly backstage before the governor’s town hall event at the University of Southern Maine. The governor shared a photo of the meeting, which included USM President Glenn Cummings, on his official social media site.

Sen. Mark Dion, D-Portland, was one of the Portland lawmakers who endorsed Strimling, citing his ability to better craft a shared vision between City Hall and the Blaine House. Dion said he was pleased the two had met, because the state’s economic health is tied to Portland’s and the city needs a seat at the table when public policy is being discussed at the state level.

“I suspect it was a pretty lively discussion,” Dion said. “I think you can be collaborative without giving up your values. I think the mayor has the capacity to do that.”