Adila is in the far east of South Darfur. Last week the government had accused the rebels of attacking the government-controlled town.
"We are looking for the pilot," said Ashr. "We have the body of the plane."
The United Nations and the African Union (AU), both of which are monitoring a shaky ceasefire in Sudan's arid west, also could not confirm the report.
In the past four years of conflict, the rebels have claimed to have shot down military transport planes and helicopters.
The rebels said the government attacked their areas around Adila ahead of a UN-African Union mediated meeting of rebel factions in Tanzania to renew the peace process.
Eight Darfur groups including JEM agreed on Monday at the Arusha talks on a platform for peace negotiations with the Sudanese government that they said could start within three months.
The unified position for the fractious rebels came after the UN Security Council last week ordered the deployment of 26,000 peacekeepers to Darfur.
According to the UN, at least 200,000 people have been killed and more than two million displaced since the conflict started in Darfur more than four years ago. Some sources say the toll is much higher.
A peace agreement was signed in May 2006 with the Sudanese government, but only one of three negotiating rebel factions endorsed the deal. The violence has since spiralled and rebel splinters have flourished.