The goal would be to "ensure that Syria has not engaged and is not engaging in undeclared nuclear activities, especially those that could contribute to a nuclear weapons program," the lawmakers said.
They also called for sanctions against any Syrian officials or entities that were found to have "received illicit nuclear assistance from North Korea and other proliferators."
Democratic Senator Kirsten Gillibrand's office made the letter public and said it had been sent on December 2.
Number-two Republican Senator Jon Kyl, Republican Senator John Ensign, Independent Senator Joe Lieberman, Democratic Representatives Ed Markey, Ed Royce, and Brad Sherman as well as Republican Representative Jeff Fortenberry signed the letter.
IAEA "special inspections" are a rarely-used tool that allows UN inspectors to request more intrusive access to sites.
The UN agency has expressed increasing impatience with Syria over gaining access to information and locations connected to an alleged nuclear site, but stopped short thus far of seeking such new inspections.
Damascus is accused of having been in the process of building an undeclared reactor at a remote desert site called Dair Alzour until it was bombed by Israeli planes in September 2007.
The IAEA has been investigating the allegations since 2008 and has already said that the building bore some of the characteristics of a nuclear facility.
UN inspectors also detected "significant" traces of man-made uranium at that site, as yet unexplained by Damascus.
In addition, the watchdog has also requested access to three other locations allegedly functionally related to Dair Alzour, but so far to no avail.
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