U.S. Senate Republican leader Mitch McConnell set a vote on a straight repeal of Obamacare after efforts to overhaul the healthcare law collapsed, but the new approach unraveled within hours on Tuesday in a sharp setback for President Donald Trump and his Republican Party.

The disarray in the Republican-controlled Senate rattled financial markets and cast doubt on the chances for getting Trump's other domestic policy priorities, such as tax reform, through a divided Congress.

Repealing and replacing Obamacare has been a top Republican goal for seven years, and Trump made the promise a centerpiece of his White House campaign. The overhaul's failure calls into question not only his ability to get his agenda through Congress but that of the Republican Party to govern effectively.

Saying he was disappointed, Trump told reporters at the White House that "we're probably in that position where we'll just let Obamacare fail."

"We're not going to own it, I'm not going to own it. ... Republicans are not going to own it. We will let Obamacare fail, and then the Democrats are going to come to us," he said.

McConnell gave up on efforts to overhaul the 2010 Affordable Care Act late on Monday after it became clear he did not have the votes. Instead, he announced plans to vote in coming days on a two-year transition to simply repeal the healthcare law with no replacement.

"We will now try a different way to bring the American people relief from Obamacare," McConnell said on Tuesday as he opened the Senate, where the Republicans hold a razor-thin 52-48 majority. "I think we owe them at least that much."

But Republican Senators Shelley Moore Capito of West Virginia, Susan Collins of Maine and Lisa Murkowski of Alaska quickly announced they would not back repeal, dooming the fledgling effort. With Democrats united in opposition, Republicans can only afford to lose two votes to pass the measure in the Senate.

(Writing by John Whitesides; Additional reporting by Caroline Humer in New York and Ginger Gibson, Richard Cowan in Washington; Editing by Tom Brown, Nick Zieminski and Jonathan Oatis)