"The Syrian foreign ministry demands the UN Security Council act immediately in the face of this aggression and take appropriate measures to prevent its recurrence," the letter added.
It said three Syrian soldiers had been killed and 13 wounded in strikes by four coalition planes on an army camp in the eastern province of Deir Ezzor.
The Britain-based Syrian Observatory for Human Rights monitor earlier said four Syrian soldiers had been killed and 13 injured.
The monitor said the strikes had hit a camp in the west of Deir Ezzor, around two kilometres (one mile) from an area controlled by the Islamic State group.
The Observatory said it was the first time a US-led coalition strike had killed Syrian government troops.
Much of Deir Ezzor province is under the control of IS, which is regularly targeted there by the US-led coalition, but the regime remains present in small areas, including in the provincial capital.
The coalition has been carrying out strikes against IS since September 2014, and does not coordinate with the government in Damascus.
The Syrian government has regularly criticised the US-led strikes as ineffective and illegal because they are not coordinated with regime forces, and the ministry that the Deir Ezzor incident was further evidence of the coalition`s failings.
"The US coalition lacks the seriousness and credibility to effectively combat terrorism," the ministry said.
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