Few things frustrate President Obama more than what he calls the “Washington playbook” — a view that U.S. military firepower is the solution to most of the toughest foreign policy problems.

Last week, 51 State Department officials wrote a letter of dissent to the administration’s Syria policy that seemed to come directly out of that playbook. At issue is how to stop the killing in Syria that has taken more than 400,000 lives and displaced millions.

“We do see merit in a more militarily assertive U.S. role based on the judicious use of stand-off and air weapons,” the officials wrote.

The dissent cable was notable for its large, if not unprecedented, number of signatories, reflecting the broad dismay and frustration inside the State Department with the policy toward Syria. It also highlights a roiling debate inside the administration over whether Obama has been too reluctant to use military power to alleviate suffering in Syria.

“I view this less as a policy document than just a declaration of frustration,” said Perry Cammack, a former State Department official in the Obama administration who is now an associate at the Carnegie Endowment for Inter­national Peace.

The diplomats’ call for using the military to strengthen Secretary of State John F. Kerry’s hand in negotiations with the Syrian regime and its backers is not likely to win much support from the White House. “While I understand the frustration, these are hardly the people the president would turn to for military advice,” Cammack said of the diplomats.

Nor is the letter likely to garner much backing from the U.S. military, which has been determined not to get pulled into Syria’s chaotic civil war.

But the cable, filed through the State Department’s dissent channel, does highlight one of the biggest foreign policy rifts in Washington, pitting the White House and the military against front-line diplomats.

The mid-level State Department officials who signed the letter have been at the center of the administration’s response to the Syrian civil war for much of the past five years. Some have served as interlocutors with U.S.-backed Syrian rebels who have struggled to stay alive on a chaotic and deadly battlefield. Others have worked to provide relief to Syrian civilians trapped in a worsening humanitarian ­catastrophe.

More than any other U.S. officials, they have seen the suffering in Syria up close. The power of the cable comes less from its policy prescriptions, which most analysts described as vague and unworkable, than its unmistakable sense of outrage. “We believe the moral rationale for taking steps to end the deaths and suffering in Syria, after five years of brutal war, is evident and unquestionable,” the letter says.

On Monday, Kerry gave the officials a tentative vote of support, declaring that their memo was “very good.”

The cable has received a much chillier reception from the White House, where press secretary Josh Earnest said the president had not read it. Obama has resisted the idea of using limited American airstrikes to punish Syrian President Bashar al-Assad for violating the cease-fire negotiated this year.

Such strikes could draw the United States into a fight with Russia, which is providing air defense systems to protect Assad’s forces. So far, the Russians have not turned their radar systems on U.S. planes.

That could change if the Americans began attacking Assad. “Could we defeat the Russian systems? Yes,” said retired Col. Ioannis Koskinas, a former Air Force strategist and a senior fellow with the New America Foundation. “But that is really serious stuff.”

It also is not clear that limited strikes could force Assad to moderate his negotiating position and submit to peace talks, and such limited interventions have a mixed record of success. “This is really one of the hardest things to do, and it is reasonable to expect that Assad will make the greatest effort to resist,” said Micah Zenko, a senior fellow with the Council on Foreign Relations who has written extensively about limited military interventions.

The White House’s current approach will do little to moderate the behavior of the Assad regime, which most analysts say has killed far more Syrians than the Islamic State. Nor will it do much to ease the concerns of critics who have described Obama’s policy in Iraq and Syria as ignoring America’s moral obligations.

“It’s one thing that we don’t hear much from the Obama administration — especially on Syria,” said Brian Katulis, a senior Middle East analyst with the left-leaning Center for American Progress. “It’s all anti-ISIL, which is an important goal, but we’ve lost sight of the broader stakes.”

The moral argument was at the heart of the State Department dissent. “We firmly believe it is time that the United States, guided by our strategic interests and moral convictions, lead a global effort to put an end to this conflict once and for all,” the diplomats wrote.

Far less clear from the four-page letter was how they planned to achieve that goal.