Omar al-Bashir warned Monday that tensions could resurface in the Abyei border region, if newly independent South Sudan did not respect arrangements governing the area, dpa reported.
Abyei was a province of Sudan, al-Bashir stressed in an interview with the BBC.
Abyei, the oil-rich border region between Sudan and the new South Sudan, failed to hold a referendum on its possible independence, and Khartoum's armed forces have moved into the area and started clashing with the Sudan People's Liberation Army.
Despite an agreement to end the fighting, neither side has formally signed an agreement.
"In the past, we were forced to fight when they (the south) tried to impose a new reality," al-Bashir said.
While expressing sadness over the division of Sudan, he told the BBC it was a price worth paying for peace.
Al-Bashir lowered his country's flag at Saturday's independence ceremony in the new South Sudanese capital, Juba.
Meanwhile, the largest rebel organization in Sudan's western crisis region of Darfur, the Justice and Equality Movement (JEM), welcomed South Sudan's independence, the daily Sudan Tribune reported.
"JEM is keen to share with our brothers in South Sudan their joy and celebration of their new state," the newspaper quoted from the statement.
The government in Khartoum bore responsibility for the partition of Africa's largest country, JEM said, as they had failed to make Sudan's unity attractive.
"They have to be aware of the lesson to avoid a repeat of the separation of another part of the Sudan," the rebel organization said in reference to Darfur.
Al-Bashir is facing an arrest warrant from the International Criminal Court for war crimes, genocide and crimes against humanity in Darfur