The so-called "dissent channel" cable urges attacks against Bashir al-Assad's regime for its persistent violations of a shaky ceasefire aimed at bringing an end to the five-year conflict.
It emerged as Russian forces bombed US-backed militia in Syria, highlighting the tangle of alliances in a war where Moscow is working to prop up its chief regional partner.
The cable, signed by working-level diplomats, demands "a judicious use of stand-off and air weapons", according to the New York Times, and lays bare the divisions in Washington policy circles.
With only seven months left in office and a clear aversion to getting bogged down in Middle East conflicts, Obama has shown little appetite for such action.
But the administration's alternative policy -- to work with Russia to secure a ceasefire in Syria's five-year civil war and talks on a political transition -- has made little headway.
That policy received a further blow when Assad's Russian allies launched raids in southern Syria, according to the Pentagon.
"Today, Russian aircraft conducted a series of airstrikes near al-Tanf against Syrian Counter-ISIL forces that included individuals who have received US support," said a senior US defence official who requested anonymity.
ISIL is an alternative name for the Islamic State Group.
"Russia's latest actions raise serious concern about Russian intentions. We will seek an explanation from Russia on why it took this action and assurances this will not happen again."
Washington and Moscow have publicly vowed to work together to persuade Assad to negotiate a settlement with his opponents, but the US has frequently expressed exasperation about what it sees as Russia's less-than-fulsome commitment.
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US policy on Syria has been criticised for ineffectiveness, after five years of brutal internecine fighting that has claimed hundreds of thousands of lives and sent many more fleeing.
American forces are engaged in Syria but are assisting local militias to fight the Islamic State jihadist group, not confronting Assad's Russian and Iranian-backed forces.
The State Department cable says Assad's continued violation of a countrywide partial ceasefire -- a cessation of hostilities -- that was negotiated in February, meant a political settlement was untenable, the Times reported.
Without consequences for the violations, the regime will feel no compunction to talk with moderate opponents, the cable said, with their barrel bombing of civilians the "root cause of the instability that continues to grip Syria and the broader region."
Photo: A fighter of Syria's Manbij military council (L) blindfolds a reported Islamic State (IS) group fighter on the outskirts of the northern Syrian town of Manbij
There were more barrel bombs in rebel areas of Aleppo on Thursday.
At least four civilians were killed in the fresh violence, three on the eastern side of Aleppo and one in the west, the Syrian Observatory for Human Rights said.
That came hours after US Secretary of State John Kerry warned Moscow that Washington's patience was running out over breaches of the nationwide ceasefire.
The Wall Street Journal said 51 mid- to high-level senior State Department officials signed the memo submitted via the "dissent channel", which allows diplomats who disagree with official policy to lodge concerns without fear of retribution.
"We are aware of a dissent channel cable written by a group of State Department employees regarding the situation in Syria," State Department spokesman John Kirby told AFP.
"We are reviewing the cable now, which came up very recently," he added.