The US Senate has passed a measure to take the first step towards dismantling President Barack Obama's health care law.

Senators were responding to pressure to move quickly even as Republicans and President-elect Donald Trump grapple with what to replace "Obamacare" with.

The near-party line 51-48 vote came on a non-binding Republican-backed budget measure that eases the way for action on repeal legislation as soon as next month.

"We must act quickly to bring relief to the American people," said Republican and Senate majority leader Mitch McConnell.

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

Mr Trump oozed confidence at a news conference on Tuesday, promising his incoming administration would soon reveal a plan to repeal Obamacare and replace it with legislation to "get health care taken care of in this country".

"We're going to do repeal and replace, very complicated stuff," he told reporters, adding that both elements would pass virtually at the same time.

That promise will be almost impossible to achieve in the complicated web of Congress, where Republican leaders must navigate complex Senate rules, united Democratic opposition and substantive policy disagreements in their own ranks.

Passage of Thursday's measure would permit follow-up legislation to escape the threat of a filibuster by Senate Democrats, but Republicans are not close to agreement among themselves on what any Obamacare replacement would look like.

Republicans plan to get legislation voiding Mr Obama's law and replacing parts of it to Mr Trump by the end of February, House majority leader Kevin McCarthy said on Wednesday. Other Republicans have said they expect the process to take longer.

The 2010 law extended health insurance to 20 million Americans, prevented insurers from denying coverage for pre-existing conditions and steered billions of dollars to states for the Medicaid health programme for the poor.

Republicans fought the effort tooth and nail and voter opposition to Obamacare helped carry the party to impressive wins in 2010, 2014 and last year.

Thursday's Senate procedural vote will set up special budget rules that will allow the repeal vote to take place with a simple majority in the 100-member Senate, instead of the 60 votes required to move most legislation.

That means Republicans, who control 52 seats, can push through repeal legislation without Democratic co-operation.

They are also discussing whether there are some elements of a replacement bill that could get through at the same time with a simple majority, but for many elements of a new health care law, Republicans are likely to need 60 votes and Democratic support, and at this point the two parties are not even talking.

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