WASHINGTON — More than 50 State Department diplomats have signed an internal memo sharply critical of the Obama administration’s policy in Syria, urging the United States to carry out military strikes against the government of President Bashar al-Assad to stop its persistent violations of a cease-fire in the country’s five-year-old civil war.

The memo, a draft of which was provided to The New York Times by a State Department official, says American policy has been “overwhelmed” by the unrelenting violence in Syria. It calls for “a judicious use of stand-off and air weapons, which would undergird and drive a more focused and hard-nosed U.S.-led diplomatic process.”

Such a step would represent a radical shift in the administration’s approach to the civil war in Syria, and there is little evidence that President Obama has plans to change course. Mr. Obama has emphasized the military campaign against the Islamic State over efforts to dislodge Mr. Assad. Diplomatic efforts to end the conflict, led by Secretary of State John Kerry, have all but collapsed.

But the memo, filed in the State Department’s “dissent channel,” underscores the deep rifts and lingering frustration within the administration over how to deal with a war that has killed more than 400,000 people.