"We will not negotiate with the South's government because they don't understand anything but the language of the gun and ammunition," Bashir, who was visiting soldiers in Heglig, said Monday, according to news agencIes.
Relations between Sudan and South Sudan reached rock bottom when South Sudan seized Heglig, Sudan's most important oil-producing area, earlier this month, only to withdraw Friday.
South Sudan claimed its abandonment of Heglig was an "orderly withdrawal," but Sudan claimed to have killed more than 1,000 South Sudanese soldiers, driving the South's army out by force. South Sudan rejected Sudan's casualty figures.
The withdrawal seemed to ease tensions slightly, but the attack and Bashir's statement Monday heated up the long-running dispute between the two countries. South Sudan seceded last July under the terms of a 2005 peace deal that ended 22 years of civil war.
Fallout from the fighting around Heglig has sparked new accusations, with each sides charging the other with damaging oil-production facilities in the area.
Sudan has accused the South's army of sabotaging oil facilities in Heglig, while the South says Sudan's military dropped bombs on oil facilities in the area during last week's fighting.
A statement released Monday by Sudan's Ministry of Foreign Affairs demanded compensation for damage to the oil-production facilities. It said that Sudan had no intention to attack South Sudan, only to defend its own territory.
A South Sudan military intelligence official, Mac Paul, said Monday's bombing amounted to a declaration of war. Sudanese military officials have denied the bombing.
The U.N. peacekeeping mission in South Sudan said it deplored the bombing of the Rubkona market near the town of Bentiu on Monday. "These indiscriminate bombings resulting in the loss of civilian lives must stop," said Hilde F. Johnson, the U.N. special representative in South Sudan.
A U.S. State Department spokeswoman, Victoria Nuland, condemned Sudanese incursions into South Sudan, calling for a halt to hostilities and a resumption of peace talks.
"We recognize the right of South Sudan to self-defense and urge South Sudan to exercise restraint in its reaction to Sudan's attack ... and to refrain from disproportionate actions, which would only further inflame the hostilities between the parties," Nuland said.
Sudan had been dropping bombs in South Sudan before last week's battle over Heglig, but South Sudan's occupation of Heglig saw a sharp escalation of the tensions between the two nations.
The secession last year left contentious issues such as border demarcation and oil transit fees unresolved. After the split, most of the oil in the region was within South Sudan.
Sudan, facing a budget crisis after losing most of its oil revenue, seized several shipments of South Sudan oil in January. The South responded by shutting down oil production.
As tensions increased, fighting flared along the disputed border. International diplomats have pressured the two sides to resume peace talks, without success.
-- Robyn Dixon
Photo: A police officer walks past the smoldering remains of a market in Bentiu, South Sudan, on Monday following a bombing by Sudanese aircraft. Credit: Michael Onyiego / Associated Press