WASHINGTON—Defense Secretary Jim Mattis urged lawmakers on Wednesday to reject a bipartisan proposal that seeks to cut off American support for Saudi Arabia’s controversial three-year war in Yemen.

In a letter to Senate Majority Leader Mitch McConnell (R., Ky.), Mr. Mattis warned that the proposal would undermine American interests in the Middle East, jeopardize the country’s partnership with Saudi Arabia and increase the risk of a regional war with Iran.

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