The resolution cites the War Powers Act of 1973 and argues that the USA military involvement in assisting the Saudi Arabia-led coalition fighting in Yemen falls under this act.
Opponents argued that the War Powers Resolution does not apply because the U.S.is not directly involved in combat in Yemen.
But the resolution will probably be struck down by Mr Trump's first veto since he took office. Should it manage to successfully pass through both the Senate and the House, it would be the first time that lawmakers have tapped on the act to cease U.S. military involvement in a foreign conflict.
Meanwhile, revelations that interests connected with the Trump administration were in negotiations to sell the Saudis nuclear technology have shed new light on the president's cozy relationship with the embattled kingdom.
The caucus initially emphasized that the resolution would end USA midair refueling for Saudi coalition warplanes, which the Donald Trump administration ended a year ago shortly after Khashoggi's murder. Mike Lee, R- Utah.More news: Google Introduces AI-based Lookout App for Visually Impaired
U.S. President Donald Trump and Saudi Deputy Crown Prince and Defense Minister Mohammed bin Salman shake hands in the State Dining Room before lunch at the White House in Washington, D.C., on March 14, 2017.
Many lawmakers also want to push Trump to demand a stronger response from the Saudi government to the murder of Saudi journalist Jamal Khashoggi at a Saudi consulate in Turkey in October.
Saudi Arabia is leading a coalition helping Yemen fight Iranian-backed Houthi rebels.
Wednesday's resolution will be considered in the now Democrat-led House of Representatives, and is thought likely to pass.
Some also contended that stopping USA support would help Iran, and potentially prolong the conflict by ending Washington's ability to influence Saudi Arabia and the United Arab Emirates, a partner in the conflict, to pursue a sustainable political settlement.
"The bottom line is the United States should not be supporting a catastrophic war led by a despotic regime with a risky and irresponsible foreign policy".More news: Some Calgary flights cancelled after Canada grounds Boeing 737 MAX jets
"We need to stay engaged (in Yemen) with the limited engagement we've had", Risch said.
"The Senate's vote to end the US role in Yemen is also a vote to re-democratize our nation's foreign policy".
The vote on the resolution appears to be one of several fault lines between Republicans and President Donald Trump on national security to emerge in recent weeks.
Democratic Senator Bernie Sanders has called the Saudi war on Yemen a humanitarian and strategic disaster.
Republican leaders argue that the resolution is too broad and sets a precedent allowing any lawmaker to force a vote to end military cooperation arrangements and USA security assistance to any country.
It is the second time the Senate has approved a measure that would curb USA military involvement in Yemen.More news: House Votes for Russia Investigation Final Report Be Public
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.