A prisoner exchange involving thousands of Syrian and Turkish captives and at least 48 Iranians was underway Wednesday morning in Damascus, according to a Turkish charity organization that has been involved in previous prisoner swaps in Syria."They are being handed over right now. We have teams on the ground in Damascus. They are at various police stations handling the exchange," said Huseyin Oruc, deputy president of the Humanitarian Relief Foundation, an organization widely known by its Turkish acronym IHH.

"We also have a team handling the handover of the 48 Iranians from the opposition. There are Turks and Syrians being released," Oruc told CNN in a phone interview.

The Syrian government was releasing 2,130 civilians, including 73 women, in exchange for the release of 48 Iranian prisoners held by rebels, IHH President Bulent Yildirim said, according to the semi-official Turkish Anatolian Agency.

A Syrian rebel spokesman said this may be the biggest prisoner exchange the rebels have conducted with their government adversaries since the start of the Syrian conflict almost two years ago.

"I myself went to two exchange negotiations," said Louai Miqdad, a spokesman for the rebel Free Syrian Army. "This is bigger."

Miqdad said the Iranian prisoners being released were members of a group abducted by rebels in Damascus last August.

The Iranian government denied rebel claims that the 48 captives were members of Iran's Revolutionary Guard. Tehran claims the 48 Iranians were Shiite pilgrims visiting a holy site in the Syrian capital.

Opposition leaders accused the Syrian government of placing the freedom of several dozen captives from its ally Iran above the release of thousands of Syrian loyalist soldiers believed to be in rebel custody.

"One Iranian person means more to him (Syrian President Bashar al-Assad) than a thousand soldiers," Miqdad said. "The command came direct from Tehran."

"The big prize for the regime is the Iranians, keeping them happy," said George Sabra, vice president of the National Coalition of Syrian Revolutionary and Opposition Forces. "The regime never cared about the lives of the civilian population or even his own armed forces."

Iranian state-run media reported that "foreign-backed militants in Syria have released 48 Iranian pilgrims." Like Syria, Iran refers to Syrian rebels as foreign-backed militants or terrorists.

Syrian state-run media has not yet reported on the prisoner exchange.

CNN's Saad Abedine contributed to this report.