Army says it killed 207 fighters near Nigerian town close to the border with Cameroon.
Chad said its warplanes bombed Boko Haram positions in neighbouring Nigeria to avenge twin suicide bombings in the capital this week blamed on the rebel group.
Chad’s military vowed it would continue its “merciless” pursuit of the armed group “so that no drop of spilt Chadian blood goes unpunished”.
“In response to the cowardly and barbaric acts perpetrated by Boko Haram terrorists… the armed forces carried out reprisal air strikes on the terrorists’ positions in Nigerian territory on Wednesday,” the military said in a statement on Thursday.
Six Boko Haram bases were destroyed in the air raids, which caused “considerable human and material losses”, it said, without giving further details.
Monday’s attacks on the police headquarters and a police academy in N’Djamena were the first in the capital of the central African country, which has taken a lead role in a regional offensive against the Nigeria-based Boko Haram.
No group has claimed responsibility but Chad and its allies immediately blamed the Boko Haram, who have carried out a series of bloody attacks in border areas of countries that share a frontier with northeastern Nigeria.
Chad on Wednesday banned the full-face veil and ordered security forces to seize burqas from markets and burn them.
“Wearing the burqa must stop immediately from today, not only in public places and schools but throughout the whole of the country,” Prime Minister Kalzeube Pahimi Deubet told religious leaders the day before the start of the holy Muslim month of Ramadan.
Any type of clothing that leaves only the eyes visible is a form of “camouflage” and is now banned, he added, asking religious leaders to spread the message in mosques, churches and other holy places.
Deubet said security forces in the Muslim majority country had been instructed to “go into the markets and to seize all the burqas on sale and burn them”.
Anyone found wearing a burqa will be “arrested, tried and sentenced in summary proceedings”, he added.