Hissene said another 212 opposition fighters were taken prisoner, 127 of their vehicles seized and 93 destroyed.
He said 22 soldiers had also died and 31 were wounded in the clashes.
The UFR, which is seeking to overthrow Idriss Deby, Chad's president, said "several dozen" government troops had been killed in clashes.
But there has been no independent confirmation of either claim.
The fighting has heightened concerns among UN agencies and aid groups caring for about 450,000 refugees from Sudan and the Central African Republic.
Am-Dam lies about 100km south of Abeche, a base used by relief agencies.
UN agencies have warned that the clashes will make it difficult to reach 22,000 refugees from Darfur in neighbouring Sudan and 60,000 internally displaced people in the area.
The UN Security Council condemned the renewed military incursions "coming from outside" in eastern Chad.
Chad's government accuses Sudan of backing the UFR rebels, who have vowed to reach Ndjamena.
|The UN warns that the clashes will make it difficult to reach refugees [AFP]
The UN statement also stressed that "any attempt at destabilisation of Chad by force is unacceptable".
The European Union and African Union have also spoken out against the rebel offensive.
Javier Solana, the EU foreign policy chief, condemned "the acts of violence by armed groups coming from Sudan in the east of Chad".
"I call on them to renounce violence and begin negotiations with the Chad government," he said.
Meanwhile, Ramtane Lamara, the African Union's peace and security commissioner, condemned "all kinds of anti-constitutional change of government, and acts of destabilisation".
UFR rebels have been fighting against Deby for more than three years.
In February 2008, they battled their way to the gates of the presidential palace in Ndjamena before being beaten back.
Adam Mustafa Ibrahim, the governor of Abeche, told Al Jazeera: "Security forces are on alert; they are patrolling the borders and control the situation.
"We do not pay attention to rumours, but if there is solid information regarding rebel movements, we will attack them as we have before."
Peace between Chad and Sudan is regarded as essential to any lasting settlement to a six-year-old uprising in Sudan's western Darfur region.