A massive US-led assault on Falluja began 10 days ago with the alleged aim of wresting control of the city from foreign fighters.
The US says the men were led by Jordanian-born Abu Musab al-Zarqawi and other fighters opposed to the US presence in Iraq.
Washington has repeatedly accused Syria and Iran of allowing
foreign fighters to cross their borders with Iraq to join the Falluja resistance.
However, al-Thawra publication said on Thursday: "The question of foreign fighters crossing Iraqi [borders] has been exaggerated, given that only 24 of the 1000 men captured in Falluja are foreign."
Of the more than 1000 men aged between 15 and 55 who were captured in intense fighting in Falluja last week, just 15 are confirmed foreign fighters, General George Casey, the top US ground commander in Iraq, said on Monday.
The US says it now controls more
than 90% of the ravaged town
Several senior commanders agree that the overwhelming majority of fighters are drawn from tens of thousands of former government employees whose sympathies lie with Saddam Hussein, unemployed criminals who find work laying roadside bombs, and Iraqi "religious extremists".
Also on Monday, interim Iraqi Prime Minister Iyad Allawi acknowledged that anti-US fighters were largely made up of his countrymen.
But he maintained that foreign fighters had often been responsible for car bombings and other spectacular attacks that he said were designed to derail elections scheduled for January.
For its part, the Syrian daily warned "the destruction of Falluja is a message sent to other Iraqi cities, threatening them with the same fate if they rebel against the occupation and hinder plans made for the Americanisation of Iraq".
"The destruction of Falluja is a message sent to other Iraqi
cities, threatening them with the same fate if they rebel against the occupation and hinder plans made for the Americanisation of Iraq"
The United States must "prove that al-Zarqawi is not a ghost who serves to cover the intentions of the American invasion, as with the question of weapons of mass destruction which was exaggerated in order to launch the Iraq war" in March 2003.
Washington slapped unilateral sanctions on Damascus in May, claiming it was supporting terrorism and seeking to develop weapons of mass destruction, charges denied by Syria.
In September, Syria undertook to tighten its 600km border with Iraq, which was closed as part of a state of emergency declared in Iraq on 7 November.
The Syrian rebuke comes after US officials admitted only about 5% of fighters recently captured in Falluja were of foreign origin.