"This resolution is an unnecessary, risky attempt to weaken my constitutional authorities, endangering the lives of American citizens and courageous service members, both today and in the future", Trump said in the veto message.
He said there were no USA military personnel in Yemen accompanying the Saudi-led coalition fighting Iran-backed Houthis, although he acknowledged that the US has provided limited support to the coalition, including intelligence sharing, logistics support, and - until recently - in-flight refueling of non-U.S. aircraft.
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 Yemen War Powers Resolution was a bipartisan, bicameral effort to end the world's largest humanitarian crisis and supported by some of the president's most trusted Republican allies", Khanna said.
A senior administration official said that Trump was involved in drafting and editing the language of Tuesday's veto statement and that he had told senators for some time he was going to issue a veto.
Congress passed a historic War Powers resolution in early April, featuring strong bipartisan support, representing much of President Trump's foreign policy vision of "America First", which contended that America should intervene less overseas and focus more on rebuilding the country.
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The four-year-long civil war in Yemen, which pits the Saudi-led coalition against Houthi rebels backed by Iran, has killed tens of thousands of people and spawned what the United Nations calls the world's most dire humanitarian crisis, with the country on the brink of starvation.
The U.S. has provided billions of dollars of arms to the Saudi-led coalition fighting against Iran-backed rebels in Yemen. The resolution had invoked the War Powers Act to distance the United States from the conflict in Yemen, which began in 2014. In the Senate the vote was 54 to 46, with seven Republicans voting with Democrats.
Pelosi added: "This conflict must end, now".
The U.S. has provided intelligence and logistical support to the Saudis since 2015. Trump vetoed that resolution last month.
International Rescue Committee president and CEO David Miliband said that vetoing the measure represents an "effective green light for the war strategy that has created the world's worst humanitarian crisis to continue". The veto was the second of his presidency, after he overrode a congressional resolution that aimed to reverse the border emergency he declared in order to secure more funding for his wall between the United States and Mexico in March.