The powerful Houthi leader, Mohammed Ali al-Houthi, who heads the so-called Supreme Revolutionary Committees, also hailed the vote and called upon other Western countries to take similar steps against what he described as "American, British, Israeli, Saudi, and Emirati hegemony over Yemen".
However, if the resolution is passed fully, it will become a historic move as it will be the first measure by the US Congress to invoke the 1973 War Powers Resolution to directly put limit on the President's use of military powers. Its backers have argued that U.S. involvement in the conflict violates the constitutional requirement that Congress alone can authorize participation in war.
Lee was among seven Republicans who joined all members of the Democratic Caucus in backing the bill.
The Senate resolution, an unprecedented attempt to curtail presidential powers, sought to end the USA military involvement in the conflict within 30 days.
McConnell argued the Yemen resolution "will not enhance America's diplomatic leverage" and will make it more hard for the U.S.to help end the conflict in Yemen and minimize civilian casualties.
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Wednesday's resolution will be considered in the now Democrat-led House of Representatives, and is thought likely to pass.
Democratic Senator Chris Murphy of CT hailed the outcome.
The resolution must still be taken up in the House, where members passed a almost identical resolution to end US participation in the Yemen war earlier this year.
Now, the Trump administration argues that its logistics support falls short of the hostility threshold the law envisions.
The 1973 law was supposed to provide a check on the growing number of global military entanglements presidents committed the U.S.to, without actually seeking a war declaration or other authorization from Congress. The conflict has killed thousands and left millions on the brink of starvation, creating what the United Nations called the world's worst humanitarian crisis.
Largely overlooked throughout this whole process is that these votes show how US foreign policy, so often a byproduct of Washington lobbyists and other powerful special interests, can be democratized.
On Thursday, the Senate is expected to vote on a resolution - already passed by the House - to reverse Trump's emergency declaration on border security, after the president went around Congress in a bid to secure more funding for his wall between the United States and Mexico.