They also argued that US involvement in Yemen violated the constitutional requirement that Congress, not the president, should determine when the country goes to war.
In a statement to the Senate on Tuesday, the Commander-in-chief called the resolution "an unnecessary, risky attempt to weaken his constitutional authorities".
The US now pours billions of dollars of arms to the Saudi-led coalition fighting against Houthi rebels, who are believed to be supported by Iran, in Yemen.
The California Democrat said that he will continue to push for a peaceful resolution to the conflict in Yemen and will continue to push for ending America's support in the war through future bills such as the National Defense Authorization Act (NDAA). Many lawmakers also criticized the president for not condemning Saudi Arabia for the killing of a Saudi writer Jamal Khashoggi, a Saudi who lived in the United States and had written critically about the kingdom. Members of Congress have expressed concern about the thousands of civilians killed in coalition airstrikes since the conflict began.
The fighting in the Arab world's poorest country also has left millions suffering from food and medical care shortages and has pushed the country to the brink of starvation.
"With Trump's veto of Bernie Sanders' and my War Powers resolution, which passed with bipartisan support in Congress, he is risking the lives of millions of Yemeni civilians to starvation, deadly airstrikes, and the war crimes of the Saudi regime", Khanna wrote.
The resolution passed the House of Representatives in April and the Senate in March, the first time both chambers had supported a War Powers resolution, which limits the president's ability to send troops into action. The Senate vote last month was 54-46.
In a statement Tuesday night, Pelosi called on Trump to "put peace before politics".
"President Trump's assertion of support to the Arab Coalition in Yemen is a positive signal", Minister of State for Foreign Affairs Anwar Gargash said on Twitter early on Wednesday.
Kaine accused Trump of turning a blind eye to Khashoggi's killing and the jailing of women's rights activists in Saudi Arabia. My Administration is now accelerating negotiations to end our military engagement in Afghanistan and drawing down troops in Syria, where we recently succeeded in eliminating 100 percent of the ISIS caliphate. McCaul said it was an abuse of the War Powers Resolution and predicted it could disrupt USA security co-operation agreements with more than 100 countries.
Trump was expected to issue the veto as the resolution was seen as a rebuke of Trump's Middle East policies.
Trump's first veto, issued last month, was of a congressional resolution disapproving of his emergency declaration.
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