Chad has accused Sudan of sending over the rebels
Chadian troops have defeated a rebel attack in the volatile east but some areas are still not under control, the government says.
Aid workers were evacuated from several displaced people's sites in areas bordering the troubled Sudanese region of Darfur this week.
The interior minister said all major towns were under control and the rebels had failed to gain any territory.
The rebels denied being beaten and said they were still advancing, reports say.
Chad has accused Sudan of sending the rebels over the border despite a truce.
There has been no word of casualties on either side.
Many observers believe the Union of Resistance Forces (UFR) group, which was formed in January, is making a last-ditch attempt to prove its relevance before the arrival of June rains makes any movement in the east impossible.
A rebel communique issued on Wednesday said the UFR's ultimate goal was to reach the Chadian capital, N'Djamena, but the mood in the city remains calm with most people going about their business as normal, the BBC's Celeste Hicks reports.
Rebels in Chad have been trying to topple President Idriss Deby for more than three years.
Interior Minister Ahmat Mahamat Bachir went on national radio to say the rebels had not succeeded in gaining any territory, even though they had moved at least 100km (62 miles) into Chad from the Sudanese border and exchanged fire with government forces.
Earlier, he said that government planes had bombed the rebels. Fighting was reported south of Goz Beida on Wednesday morning.
Estimates of the number of rebel vehicles in Chad range from 50 to 200, and UN sources say two separate groups appeared to be on the move - around Goz Beida and also further south in the forested, unpopulated area that borders the Central African Republic.
A government spokesman, Mahamat Hissein, told the BBC on Thursday that there had been no heavy fighting since Wednesday evening.
"The government is in a position to stop the invasion and the invaders are always going backwards and forwards to find a new way to continue," he said.
Asked by the Network Africa programme why aid workers were asking to be evacuated, he replied: "We don't have military in all the towns and the NGOs [non-government organisations] are deployed even outside of these towns and are not secured by the army."
An e-mail received by AFP news agency from an unnamed rebel leader on Thursday said the UFR was still advancing and all was going according to plan.
Another unconfirmed statement from the rebels, quoted by AP, says they seized 12 military vehicles mounted with machine-guns in fighting on Tuesday.
Amid concern about rebels passing through the area, Irish troops working for the UN peacekeeping mission Minurcat evacuated about 50 NGO workers from a camp for displaced people south of Goz Beida.