Al-Bashir was apparently reacting to a demand by a powerful tribe that its territory in Abyei be ceded from Western Kordofan state and be made part of the southern state of Bahr al-Ghazal.
"Abyei has never been part of Bahr al-Ghazal and will therefore remain part of Kordofan," al-Bashir said in a nationally televised speech marking a military anniversary from Al Ubaid, capital of North Kordofan state.
The president said the move would wreck administrative boundaries set up when Sudan obtained its independence in 1956.
"We will not accept any amendment to those boundaries," said al-Bashir.
The Al-Ayam daily earlier reported that a branch of the powerful Dinka tribal confederation, which is very strong in Abyei, had demanded the area should become part of Bahr al-Ghazal.
Khartum and the rebel Sudan People's Liberation Army (SPLA) last year signed a preliminary accord at peace talks in Kenya, granting the south a six-year period of autonomy, at which point a referendum on self-determination would be organised.
Under the terms of the Machakos accord, if Khartum agreed to cede the Dinka territory, it would effectively extend the region to be granted self-rule and Abyei would fall into the hands of the south.
Abyei, along with two other contested regions - the Nuba Mountains and the southern Blue Nile - are among the main stumbling blocks to a comprehensive peace deal the sides have committed to signing by the end of the year, to end Africa's longest-running civil war.
The contested region lies in the south
of the country
Parts of all three contested areas are controlled by the government and parts by the SPLA.
The rebels have long claimed Abyei, whose residents fought alongside it for much of the civil war.
The war takes place against a background of domination of the mainly, though not exclusively, black African, animist south by the Arab, Islamic north, but has become increasingly driven by a fight for control of natural resources, notably oil.
Coupled with famine and disease, the conflict has claimed at least 1.5 million lives, with at least another four million displaced, according to humanitarian sources.
The Dinka is the country's biggest Nilotic tribe. They are scattered across the country, but are dominant in Bahr al-Ghazal.
SPLA leader John Garang is a Dinka from the Bor branch, located mainly in Jonglei, to the east of Bahr al-Ghazal.