The vote tally was 216-214, with all Democrats opposed.
The ritual is one of the most somber duties of a commander-in-chief.
In a video message posted on X, Mamdani said that "it is clear" his administration does not have the independent legal authority to execute the International Criminal Court's arrest warrant of Netanyahu.
President Donald Trump pledged to help Lebanon "a lot" during a White House meeting on Tuesday with the country's leader, Joseph Aoun.
A U.S. soldier killed in Iraq during a controlled detonation of an Iranian drone was a 30-year-old father from North Carolina who had served for nearly a decade.