Mahamat Hissene, the Chadian communications minister, said that 150 rebel fighters were captured, including the group's senior commander.
The Chadian army has bombarded the rebel forces since they crossed into the country from Sudan on Monday.
Ali Ordjo Hemchi, a spokesman for the UFR, told the AFP news agency that there had been new "violent clashes" on Friday.
He said that "several dozen" government troops had been killed or wounded and tanks destroyed in fighting around Houaich, near Am-Dam.
In February 2008, a rebel group battled its way across Chad to the presidential palace in Ndjamena before being pushed back by government forces.
The United Nations Security Council is to meet later on Friday to discuss the situation in the country.
UN agencies have warned that the clashes will make it increasingly difficult to reach 22,000 refugees from Darfur in neighbouring Sudan and 60,000 internally displaced people in the area.
The UN high commissioner for refugees (UNHCR) has moved 18 of its staff away from the conflict zone, with two staff remaining to ensure basic supplies and services continued, Ron Redmond, spokesman for the UNHCR, said.
"Reduced humanitarian activities can only be sustained for a short while and we are hoping to regain access to the Koukou area very soon," he said.
UNHCR runs 12 camps in eastern Chad, mainly along the remote Chad-Sudan border.
The UN World Food Programme has also pulled workers out of the region because of the security situation.
The fighting came just days after Chad reached a deal with Sudan, which it has previously accused of backing armed groups seeking to overthrow the government in Ndjamena, to refrain from using force to resolve their conflicts.
Previously, Ndjamena had accused Khartoum of sending armed groups into the east, close to the shared border of the two oil-producing countries. Khartoum denied the accusation.
Chad and Sudan resumed shaky diplomatic ties in November after previously cutting them in May.
Khartoum has accused Idriss Deby, the Chadian president, of involvement in an attack on the Sudanese capital by Darfur rebels on May 11, 2008.
Asked to comment on the implications of the latest clashes for Chad's relations with Sudan, Ahmat Mahamat Bachir, the interior and security minister, told the news conference: "The government will draw all the consequences of it."
The UN Security Council on Friday unanimously condemned the ongoing military incursion.
All 15 ambassadors endorsed a non-binding, French-drafted statement that "condemns the renewed military incursions in eastern Chad of Chadian armed groups, coming from outside."
The text stressed that "any attempt at destabilisation of Chad by force is unacceptable" and demanded that "rebel armed groups cease violence immediately and calls on all parties to reengage in dialogue" in the framework of an inter-Chadian peace deal reached in Libya in October 2007.