Updated

The Senate early Thursday passed a measure to take the first step forward on dismantling President Barack Obama's health care law, responding to pressure to move quickly even as Republicans and President-elect Trump grapple with what to replace it with.

The nearly party-line 51-48 vote came on a nonbinding Republican-backed procedural budget vote. Committee action to write repeal legislation could come to a vote next month. A full replacement would follow sometime after that, presuming Republicans can come up with one, the Associated Press reported.

"We must act quickly to bring relief to the American people," said Senate Majority Leader Mitch McConnell, R-Ky.

The House is slated to vote on the measure on Friday, though some Republicans there have misgivings about setting the repeal effort in motion without a better idea of the replacement plan.

Trump said at a news conference on Tuesday that his incoming administration would soon reveal a plan to both repeal so-called Obamacare and replace it with legislation to "get health care taken care of in this country."

The Associated Press contributed to this report