Gov. Charlie Baker is urging patience after being sworn in for his second term as the state's chief executive.

In his second inaugural address, on Thursday, the 62-year-old Baker spoke of unfinished work in education, transportation, housing and health care.

Senate President Karen Spilka administered the oath of office to the Swampscott Republican before a joint session of the Legislature, almost two months after easily vanquishing his Democratic challenger, Jay Gonzalez, in the general election.

In his remarks, Baker said many of the issues that have been tackled by state leaders have taken time.

"We have the highest rate of health care coverage in the nation. But the story was written across two decades, 10 legislative sessions, five governors and four presidents," Baker said, adding that the state's gun laws and K-12 education system have also been works in progress. "This story was written by a large cast of leaders and contributors across decades of deliberation and action."

Baker is sworn in by Senate President Karen Spilka in the House Chamber as his wife Lauren, center, and his father, Charles D. Baker, watch. (Jesse Costa/WBUR)

In his address, the governor called for changes in the state's foundation education budget.

"[W]hen it comes to the difference in performance between urban and suburban school districts, we can and must do better," said Baker, who promised to propose updates to the funding formula when he files his budget recommendation later in January. He added the budget will also include "opportunities for underperforming school districts to invest ... in proven best practices such as acceleration academies, professional development, after-school enrichment and leadership development programs."

The governor also committed to "continue to invest in public transportation," reiterating that the MBTA plans to spend over $8 billion on infrastructure over the next five years, but acknowledged it would be no small task.

"One of the reasons previous administrations didn’t invest in the core system is the complexity of upgrading and modernizing a system that operates 20 hours a day, seven days a week," Baker said. "The constant tug between getting people where they need to go and disrupting that system to make it better is a big challenge. But it’s one that must be identified, scoped and overcome."

Baker also promised to work on "delivering a big increase in housing production," as well as try to limit rising health costs.

Baker's address was well received by Democratic legislative leaders.

"I was very happy to hear education funding being on the top of both of our agendas, [and] health care and transportation," said Spilka, of Ashland. "I agree we need to tackle transportation and I believe there is a sense of urgency with that."

"Many of the items the governor brought up today were on my radar screen," said House Speaker Robert DeLeo, of Winthrop.

One of those items is the public education funding formula. Talks between the House and Senate on addressing the formula broke down last year before it could be resolved, and DeLeo hinted one reason may have been that the governor had not weighed in on the issue.

"[A]s opposed to last session, I am hopeful that maybe that [the governor's input] might make things a little bit better, to see exactly where he is coming from on this important subject," DeLeo said.

Charlie Baker and his wife, Lauren, arrive at the Mass. State House. (Jesse Costa/WBUR)

Baker enjoyed high popularity ratings throughout his first term, and often came out on top in polls as the most popular governor in America. A rare Republican in a state government dominated by Democrats, Baker has developed a good working relationship with legislative leaders in order to pass some of his agenda items, including bills aimed at helping those suffering from opioid addiction.

Baker also used his address to tout other past accomplishments. "Massachusetts no longer has a structural budget deficit," he said. "In fact, we ended last year with a major budget surplus. [We] deposited over $650 million into our stabilization fund and anticipate making another major deposit to that fund at the end of this fiscal year. And we did it without raising taxes."

Still, the chairman of the Massachusetts Democratic Party, Gus Bickford, issued a statement charging Baker has fallen short on promises in many areas, including public transportation, public education and environmental policies.

"Too many families in Massachusetts are still waiting for Governor Baker to deliver on his promises," Bickford said. "As he begins his second term as our Governor, the Massachusetts Democratic Party wishes Governor Baker the best, and will continue to hold him accountable for the promises he has made to the residents of our Commonwealth."

Following the official inauguration ceremonies at the State House, Baker will attend a celebration in Boston Thursday night, as well as two more galas in Worcester and Springfield on Friday.