President Donald Trump is prodding his military advisers to agree to a more sweeping retaliatory strike in Syria than they consider prudent, and is unhappy with the more limited options they have presented to him so far, White House and other administration officials said.

In meetings with Secretary of Defense Jim Mattis, Mr. Trump has been pushing for an attack that not only would punish the Syrian regime but also exact a price from two of its international patrons, Russia and Iran, a White House official said.