The crew said they thought they were carrying oil-drilling equipment, rather than explosives, rocket-propelled grenades and components for surface-to-air missiles, as the Thai government initially reported.
That contradicts a report from arms-trafficking experts.
Details under wraps
Full details of the weapons and where they were manufactured have not been disclosed.
"We need more time to investigate and interrogate," Sompot Khempeth, a police major, said after the Bangkok Criminal Court accepted a police request to extend the crew's detention an additional 12 days.
They can be held up to 84 days.
The crew members were not present at court and were to be informed of the ruling via video conference later in the day, Sompot said.
Thai authorities, acting on a US tip, impounded the Ilyushin Il-76 cargo aircraft on December 12 during a refuelling stop in Bangkok.
They seized the weapons and transferred them to a Thai military base for inspection.
The Thailand government has been investigating the arms cache and says it will send the results to the UN.