It was previously reported that a Thai court had put off the hearing to July 28 as the lawyer representing Viktor Bout's interests had developed "a heart problem."
"The hearing has been postponed due to the illness of Viktor Bout's Thai lawyer," Yan Dasgupta said.
Thailand received in early May a formal request from Washington to extradite Bout to the U.S., where he has been indicted on charges of conspiracy to kill Americans.
Viktor Bout, 41, was arrested in March in Bangkok during a joint police operation led by agents from the U.S. Drug Enforcement Administration (DEA).
DEA prosecutors claim that Bout conspired with others to sell millions of dollars worth of weapons to the Revolutionary Armed Forces of Colombia, a leftist group listed by the U.S. as a terrorist organization.
If convicted, he could face life imprisonment or, at the very least, a long prison term.
Western law enforcement agencies consider him to be "the most prominent foreign businessman" involved in trafficking arms to UN-embargoed destinations.
UN reports say Bout set up a network of more than 50 cargo aircraft around the world to facilitate his arms shipments.
U.S. authorities took measures against Bout in 2005, freezing his bank accounts and submitting a list of 30 companies linked to Bout to the UN Security Council Sanctions Committee.
