Government forces shot down a Libyan warplane Monday over the town of Fada in northeastern Chad, the army said in a statement broadcast on government radio.
It said the Soviet-made MIG-23 was downed at about 5 p.m., but it gave no details.
Libyan planes have been making "blind bombardments of the civilian population" at Zouar in northwestern Chad, and the armed forces were "more determined than ever to deliver ever harsher blows to the savage Libyan horde," according to the statement.
In Paris, the French government said it is studying an "appropriate response" to Libyan air raids in southern Chad, and the Chadian Embassy there said that Libyan planes flew over towns deep in southern Chad on Sunday.
France's Defense Ministry said that Libyan planes bombed southern Chad over the weekend, but it could not confirm the reported Sunday overflights. France supports the Chad government.
Chad's embassy said that a Soviet-built Tupolev 22 bomber was seen over Sarh, one of Chad's southernmost towns near the border with the Central African Republic, and over Abeche, the major town between the capital of N'Djamena and the Sudanese border. A group of four MIG-23s also flew over Abeche, the embassy said.
In an interview published Monday in Paris, Libyan leader Moammar Kadafi conceded for the first time that Libyan troops are now in Chad. But he insisted that they number only "a few hundred," trying to free about 20 Libyan technicians he said were taken prisoner by former Chadian rebels.