Djidda Moussa Outman, Chad's secretary of state for foreign affairs, summoned Sudan's ambassador to deliver a strong protest and call on Khartoum to stop the attacks, which Chad says has caused heavy material damage.
A communique signed by Hourmadji Moussa Doumgor, a Chadian government spokesman, read: "The Chadian government reserves the right to use all available means to assure the defence of its territory."
Brigadier Osman al-Aghbash, spokesman for the Sudanese armed forces, has denied committing any violations at the Chadian borders.
"The Sudanese air force did not conduct any activities in the area lying between Sudan and Chad," he said.
Chad and Sudan have long accused each other of supporting rebel groups fighting against their respective governments.
This is the second time in five months that Chad has accused Sudan of bombing its territory.
In October, N'Djamena said four Sudanese aircraft bombed four border towns.
Khartoum dismissed the statement as propaganda.
At a summit last month convened by Muammar Gaddafi, the Libyan president, Chad and Sudan agreed not to interfere in each other's internal affairs and "refrain from any hostile activity against one another".
It was their third such agreement in 12 months.
Some analysts fear that violence spilling over from Darfur may destabilise the wider region, fuelling rebel activity in neighbouring Central African Republic.
John Holmes, the UN's new humanitarian and emergency relief co-ordinator, is in Sudan and is due to travel to Chad and the Central African Republic in the next 10 days.
About 230,000 refugees from Darfur have taken shelter in camps in eastern Chad in the past four years, where there has been renewed ethnic strife since October.