Democratic Rep. Eliot Engel of NY, chairman of the House Foreign Affairs Committee, voted to end USA military assistance to the war, saying the humanitarian crisis in Yemen triggered "demands moral leadership".
The U.S. has provided billions of dollars of arms to the Saudi-led coalition fighting against Iran-backed rebels in Yemen.
On Tuesday, several Democrats expressed their disappointment after Trump vetoed the congressional resolution.
Tuesday's veto was the second of Trump's presidency.
The CIA has concluded that Crown Prince Mohammed bin Salman, the country's de facto ruler, ordered Khashoggi's killing. And as American weapons and technology have aided the war effort, thousands of Yemeni civilians have been killed in air strikes, though the administration says it is working to reduce unintended casualties.
Mr. Kaine also accused Trump of ignoring other Saudi human-rights violations such as the killing of columnist Jamal Khashoggi at the Saudi consulate in Turkey and the jailing of feminist activists.
The president also said that the measure would harm bilateral relations and interferes with his constitutional power as commander in chief. "First and foremost, it is our duty to protect the safety of the more than 80,000 Americans who reside in certain coalition countries that have been subject to Houthi attacks from Yemen".
The resolution's approval in both the House of Representatives and the Senate had been seen as a historic milestone already, as it was the first time that a bill invoking the 1973 War Powers Resolution reached the president's desk.
House Speaker Nancy Pelosi denounced Trump's veto, saying it would serve to "perpetuate America's shameful involvement in this heartbreaking crisis". The Senate vote last month was 54-46.
Pelosi added: "This conflict must end, now". "I hope my colleagues will show we won't tolerate the Trump administration's deference to Saudi Arabia at the expense of American security interests by voting to override this veto", Kaine said.
Just last month he overrode a congressional resolution that aimed to reverse the national emergency he declared in order to obtain funding for wall at the Mexican border.
United Arab Emirates Minister of State for Foreign Affairs Anwar Gargash reacted swiftly to Trump's veto. Vetoing the measure is an "effective green light for the war strategy that has created the world's worst humanitarian crisis to continue", said International Rescue Committee president and CEO David Miliband.