Both sides claimed victory in the clash, which reportedly began when three army columns attacked a rebel hideout near the town of Biltine.
Unconfirmed reports say hundreds of men were wounded or killed in the battle that lasted several hours.
Rebels launched a campaign earlier this year aimed at overthrowing Chad's President, Idriss Deby.
Saturday's battle between rebels and government troops was extremely fierce, with many reportedly dead and wounded on both sides, says the BBC's Stephanie Hancock in Chad's capital, N'Djamena.
Dozens of wounded soldiers were taken to the main eastern city of Abeche, where scenes at the local hospital were described by aid workers as carnage, our correspondent says.
Mahamat Nouri, head of the rebel group Union of Forces for Democracy and Development, told the BBC that 300 government soldiers were killed in the fighting.
He said about 50 of his men had been killed, with many wounded.
The government in N'Djamena denies the rebels' version of events.
Defence Minister Bichara Issa Djadallah said he could not give figures of how many rebels were killed, our correspondent says.
But he was adamant that his troops had won the battle and said that government soldiers continued to encircle the rebels.
The UN says about 90,000 Chadians have been displaced by the recent fighting.
The Chadian government has accused Sudan of backing the rebels - a charge Sudan denies - while Chad denies Sudanese claims that it supports black African rebels in Darfur.Güncelleme Tarihi: 20 Eylül 2018, 18:16