Ahmed declined to comment on whether Sudan planned to retaliate, saying: "We are considering all options."
Chad late on Friday hit back at Sudanese accusations saying Khartoum was "the robber who cries thief".
Mahamat Hissene, a government spokesman, told reporters that Chad "is surprised to learn that the regime in Khartoum is protesting against action by the Chadian air force on Sudanese territory.
Hissene said that any confrontations would be "simply the consequence of the attack on Chad organised by Sudan, using mercenaries armed, trained, financed and directed by satellite by the Khartoum regime".
Both countries have regularly accused each other of backing fighters bent on overthrowing their respective governments.
Ahmed said Sudan's foreign ministry had called in Chad's ambassador to demand an explanation for the two sorties and had informed the Khartoum-based ambassadors of the five permanent members of the UN Security Council.
"Three warplanes have crossed the borders to an area south of El Geneina [the capital of Sudan's West Darfur] which is 60km inside Sudanese territory," Ahmed said earlier on Friday.
"It happened at 10.30am and 1.30pm ... It is a violation of our territorial sovereignty. Sudan is in a position to defend its territory," he said.
Chad accused Sudan of backing an armed incursion into its territory last week, after the two countries had signed a pact in Doha, Qatar, in which they had agreed to normalise relations and reject any support for rebel groups hostile to either of them.
Chad said it had stopped the advance, after clashes that killed 125 fighters.
Sudan denied involvement in the raid, saying it was a confrontation between Chad's government and "opposition groups".
Chad and Sudan resumed shaky diplomatic ties in November after cutting them in May 2008.
Sudan has accused Idriss Deby, the president of Chad, of being involved in an attack on the Sudanese capital by Darfur rebels on May 11, 2008.