Republican Governor-elect Charlie Baker and Democratic legislative leaders are promising to work together to address the state's most pressing issues despite their political differences.

Following private meetings at the Statehouse on Monday morning, legislative leaders praised the governor-elect as ready to hit the ground running on fiscal and other issues. Baker was a cabinet official in two previous administrations.

Baker says his first priorities remain building a transition team and developing his first state budget. He has been meeting political leaders in the overwhelmingly Democratic state since his narrow victory over state Attorney General Martha Coakley on Nov. 4.

Last week, he met with outgoing Gov. Deval Patrick and visited politicians and business leaders in western and central Massachusetts. Baker enters the governor's office in January.