WASHINGTON — Senate Republican leaders, after meeting with Vice President-elect Mike Pence, said on Tuesday that they would move immediately next month to start repealing the Affordable Care Act, despite qualms among some of their members.

“The Obamacare repeal resolution will be the first item up in the new year,” said Senator Mitch McConnell, Republican of Kentucky and majority leader.

Republicans have not fleshed out a plan to replace the 2010 health care law, President Obama’s signature legislative achievement. But on Tuesday they laid out their principles for a replacement plan and said they would try to minimize disruption for the 20 million people who have gained coverage under the law.

Senate Republican leaders appeared to agree with House Republican leaders on a “repeal and delay” strategy, which could keep parts of the health law in place for several years, as Congress works with the administration of Donald J. Trump to devise a replacement.