BOSTON —During his campaign for governor, Charlie Baker repeatedly criticized Martha Coakley for defending the state against a lawsuit brought by a New York children’s rights group, saying she should have settled the suit instead.

Asked this week if he would try to negotiate the case when he becomes governor in January, Baker indicated a shift since the heat of the campaign by adopting a more measured tone.

Baker said he’d meet with the group but declined to say whether he would seek to settle the lawsuit, which charged that the state Department of Children and Families was violating the constitutional rights of foster children.

“I’m not intimately familiar with the details of the case, and the case is currently being heard before a judge and I don’t want to speak before I know more about the consequences associated with that,” Baker told reporters Thursday.

During the campaign Baker said he was troubled that Coakley didn’t recommend settling despite “overwhelming evidence that there were problems in the department, which were borne out by a series of tragedies over the past couple of years.”

Baker’s latest comments not only reflect an inevitable transition from feisty campaign rhetoric, but they may give Massachusetts residents a hint of Baker’s style of governing.

Baker has portrayed that approach as pragmatic, drawing ideas from fellow Republicans and Democrats alike.

Baker’s shift away from campaign mode can also be heard in his discussion of President Obama’s health care law and Massachusetts’ botched rollout of a new health care website.

During the campaign, Baker said he would “fight for a waiver from the federal health law to protect Massachusetts’ exemplary health system.”

This week, Baker said he still wants to ensure that Massachusetts has as much flexibility as it needs on health care, but was waiting to see if the rollout of the revamped website – set for Saturday – goes smoother.

“I’m going to be looking the same thing everybody’s looking for, which is to see if the thing works or not,” Baker said, adding that he was assured by Gov. Deval Patrick in a one-on-one meeting after the election that the website is up to the challenge.

Saturday is the start of the new federal open enrollment period.

Although he won’t say if he’ll still pursue a comprehensive waiver from the federal law, Baker did say that other states have been granted waivers “of one sort or another” attached to the law.

“I just want Massachusetts to continue to be able to chart its own destiny to the extent that it can when it comes to decisions around health care,” Baker said.

“My big fear with this thing from the beginning is that all the decision-making that involves a very important issue here in the commonwealth is going to be driven by Washington and that Massachusetts is going to lose its ability to chart its own course,” he added. “I still think we should be pursuing flexibility.”

Baker won a five-way race to win Beacon Hill’s top post.

As he gears up to take office, Baker has highlighted other initiatives, from trying to reduce the number of homeless families living in hotels to zero to exploring job training programs as part of the state’s unemployment aid programs.

“We’re going to be a very high-minded administration,” he said. “We’re basically going to play by the rules.”