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He added his army would respond to any possible "provocation" from the army of South Sudan, due to become an independent state on 9 July.
Northern troops seized the territory after southern forces had ambushed a convoy of its forces in the area, killing 22 people.
Analysts fear the the dispute could reignite the north-south conflict, in which some 1.5 million were killed.
The status of Abyei was left undecided in the 2005 peace deal and a referendum, due in January, on whether the area should be part of the north or south has been postponed indefinitely.
'War crimes'
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President Omar al-BashirSudan is not greedy for the carrot of America, and does not fear from its stick”
The two sides fought for decades before agreeing to share power and hold a referendum on southern independence.
"Abyei is northern Sudanese land," President Bashir said, according to Reuters, adding: "We will not withdraw from it."Referring to US warnings that the seizure could jeopardise billions of dollars of possible debt relief and moves to drop sanctions, he said:
"Sudan is not greedy for the carrot of America, and does not fear from its stick."
On Tuesday, a southern minister in Sudan's national government resigned, saying "war crimes" had been committed in the region.
Luka Biong Deng, a senior official in the south's ruling party, originally from Abyei, said he could no longer work with Mr Bashir's party in the unity government.
Some 20,000 people have now fled the town of Abyei, which has been left deserted, aid workers say.
UN human rights chief Navi Pillay said she had received reports that northern forces had been shelling and bombing civilian areas.
The UN Security Council, which toured Sudan earlier this week, has urged northern forces to withdraw.
The US envoy to Sudan, Princeton Lyman, has warned that the takeover of Abyei put at risk moves to cancel billions of dollars worth of Sudan's debt.
He also said that Washington would find it difficult to remove Sudan from its list of state sponsors of terrorism unless troops were withdrawn from Abyei.
Under these sanctions Sudanese companies are banned from using US currency - a major obstacle to international trade.
The US has previously suggested that a peaceful transition to independence for the south and a negotiated solution to the separate conflict in Darfur could normalise relations.
Sudan: A country divided
The great divide across Sudan is visible even from space, as this Nasa satellite image shows. The northern states are a blanket of desert, broken only by the fertile Nile corridor. Southern Sudan is covered by green swathes of grassland, swamps and tropical forest.
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