Syrian Foreign Minister Walid Muallem made the comments as jihadists from the Islamic State group advance in Syria and neighbouring Iraq, where Washington is already carrying out air strikes.
"Syria is ready for cooperation and coordination at the regional and international level to fight terrorism and implement UN Security Council resolution 2170," Muallem said.
The resolution, passed earlier this month, seeks to cut funds and the flow of foreign fighters both to the Islamic State and to Al-Qaeda's Syrian affiliate, Al-Nusra Front.
And he said Damascus was prepared to work with the United States and Britain. "They are welcome," he said.
But he said any military action inside Syrian territory must be carried out in coordination with the government and respect the country's sovereignty.
"We must feel that the cooperation is serious and not double standards".
"Any violation of Syria's sovereignty would be an act of aggression," he said.
Asked if Syria's air defences could shoot down US planes, he said "that could happen if there was not prior coordination."
There would be "no justification" for strikes on Syrian territory "except in coordination with us to fight terrorism."
Muallem's comments come amid rising concern in the international community about the growing power of IS, which has declared an Islamic "caliphate" in the large stretches of territory it holds in Syria and Iraq.
The United State began carrying out air strikes in Iraq on August 8, in bid to halt the group's advances close to the Kurdish regional capital Arbil.
But, in Syria, IS has continued to advance, taking territory from both armed opposition groups in northern Aleppo province, and from the Syrian army in northern Raqa province.
The capture of the base puts the group in control of an entire province for the first time, including the provincial capital which has become a stronghold for its jihadists.
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