WASHINGTON — The House voted overwhelmingly on Tuesday to impose a series of sweeping sanctions on Turkey over its brutal assault on the Kurds in northern Syria, dealing its second bipartisan rebuke to President Trump this month for pulling back American forces to allow for the Turkish incursion.

The measure drew broad support from Republicans, including the party’s leaders, underscoring how Mr. Trump’s decision to effectively surrender American influence in the region and abandon Kurdish fighters has provoked the most vocal and intense criticism of the president by his own party since he was elected. The vote was 403 to 16, with 15 Republicans and one Democrat, Representative Ilhan Omar of Minnesota, voting against the legislation.

This month, two-thirds of House Republicans joined with Democrats to censure his withdrawal of troops from Syria in a 354 to 60 vote. It was, at the time, the most significant bipartisan repudiation of Mr. Trump since he took office.

The top Democrat and Republican on the Foreign Affairs Committee — Representative Eliot L. Engel of New York, the chairman, and Representative Michael McCaul of Texas — sponsored the legislation that passed Tuesday, which is an attempt by lawmakers to add teeth to what they consider an insufficient response from the Trump administration to Turkey’s bloody offensive into Syria. If enacted, it would prohibit the sale of arms to Turkey for use in Syria, impose sanctions on senior Turkish officials for their role in the military offensive against the Kurds, and require the administration to impose additional sanctions for the Turkish government’s purchase of surface-to-air missile systems from Russia.