General Al-Tayeb al-Musbah, of the Sudanese army, told the state-run Suna news agency that the army destroyed "scores of Jem vehicles" during the fighting.
But a Jem spokesman denied both the claims that 300 of the group's fighters had been killed and that Jem rebels had killed scores of government soldiers.
Tahir El Fakir, the speaker of the legislative assembly for Jem, told Al Jazeera from London that Jem killed two army commanders and that the rest were militia allied to the military.
"It's a ridiculous claim for the defeated to come up with such allegations. On the contrary, the Sudan armed forces and its militias have been summarily defeated. Jem lost only two and six injured.
"[The fighting] is an escalation of what has been going on - that the Sudan government is going only for a military solution.
"What we want is a peaceful solution."
Violence has been increasing in Darfur in recent months. The United Nations said that nearly 600 people were killed in the region in May, making it the bloodiest month in Darfur in nearly two years.
Fighting has been particularly heavy around the Jebel Moon region, where more than 150 people were killed in a single battle.
The renewed fighting is one reason why peace talks between Jem and the government were suspended in May.
Ibrahim Gambari, the head of the joint African Union-United Nations mission in Darfur, this week urged all parties to join the peace process, saying that the search for peace has gained momentum.
He spoke in Qatar three days ago at a round of talks aimed at finding a way to resolve the conflict.
Cause for optimism
Kemal Saiki, director of communications for the AU-UN mission in El Fasher in Darfur, said Gambari and the rest of the mission have cause for optimism.
"We have good hope that those who are still not participating at some point will decide to join the negotiations. This is what our special representative wants to see happen," he told Al Jazeera.
But Saiki said Gambari has also expressed concern about a recent increase in violence and clashes in the region between government forces and rebel movements.
"[Gambari] has taken the opportunity to appeal to all belligerent parties to cease and desist from violence and try to resolve the situation through political means and negotiation.
"But as far as a mission, we cannot confirm the [casualty] numbers. We know for a fact that there have been clashes but ... we are not in a position to verify these figures."
Darfur, which is about the same size as France, has been gripped by civil war since ethnic minority rebels rose up against the Arab-dominated government and their supporters in 2003.
About 300,000 people have died and 2.7 million fled their homes because of the violence, according to UN figures. Khartoum disputes these claims, saying that 10,000 people have been killed.