"I found it an extremely interesting conversation and to be continued, and I'm just going to leave it at that," Gore told reporters after talks with the Republican billionaire at Trump Tower in New York.
The transition team announced Monday that Gore would meet Trump's daughter, Ivanka, a close adviser to her father seen as a possible conduit for Democrats into the Trump orbit.
Gore said he had met Ivanka first, but that he spent the bulk of his time with the incoming president.
"I had a lengthy and very productive session with the president-elect," he said. "It was a sincere search for areas of common ground."
It was Trump's highest-profile announced meeting with a leading Democrat since his shock victory over Hillary Clinton in the general election last month.
Gore, who was Bill Clinton's vice president, narrowly lost the presidential election to George W. Bush in 2000 and campaigned for Hillary Clinton in her bid to become America's first female leader.
As chairman of The Climate Reality Project non-profit, he devotes most of his time to solutions for the climate crisis.
Trump first suggested he might be willing to support global accords on climate change last month, telling The New York Times he had "an open mind."
"We're going to look very carefully," he said in an interview with the newspaper, appearing to soften his campaign promise to pull the United States out of agreements such as last year's COP21 Paris Agreement, which would bind countries to reduce greenhouse gas emissions.
On the campaign trail earlier, Trump had repeatedly promised to tear up international climate agreements.
As far back as in 2012, he tweeted what would later become one of his main campaign messages: "The concept of global warming was created by and for the Chinese in order to make US manufacturing non-competitive."
Trump also told the Times that he thought there was "some connectivity" between human activity and climate change.
"Some, something. It depends on how much," he said, adding that he would still remain concerned about how much green measures would "cost our companies."
