President Omar al-Bashir issued a resolution declaring the emergency in the border states of South Kordofan, White Nile and Sennar, the official SUNA news agency said. Other parts of the border were already under a state of emergency.
The measure suspends the constitution and imposes a trade embargo against the South.
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Commerce across the frontier has unofficially been banned since South Sudan's independence last July, but the emergency formalises that prohibition.
Bashir's resolution "gives the right to the president and anyone with his mandate" to establish special courts, in consultation with the chief justice, SUNA said.
The courts will handle criminal and "terrorist" cases, it added.
Nationalist feeling has intensified in Sudan after South Sudan occupied the north's main Heglig oil field for 10 days, a move which coincided with Sudanese air strikes against the South.
It was the most serious fighting since the South's independence and raised fears of a wider war.
Sudan declared on April 20 that its troops had forced the Southern soldiers out of Heglig, but the South said it withdrew of its own accord in line with international calls.
During the Heglig occupation, Bashir threatened to overthrow South Sudan's "insect" government.
Norway's ambassador expressed concern on Sunday that he and other diplomats had not been able to meet the four foreigners detained by Sudan's army along the tense southern border.
"We have still got no access," Jens-Petter Kjemprud told AFP, adding that Norway was in close touch with South African and British officials over the four.
Sudan's army said on Saturday it arrested them in Heglig as they collected "war debris for investigation."
Kjemprud said repeated requests had been made for access to the captives. "We are concerned and would like to see these citizens as soon as possible," the ambassador said.
Jan Ledang, country director for the Norwegian People's Aid (NPA) mission in South Sudan, identified one of them as its employee John Sorbo.
A South African demining company said two of its workers were also among those abducted by the Sudanese military while on a UN landmine clearance contract in South Sudan.
Ashley Williams, CEO of state-owned Mechem, said its employees, South African Thabo Siave and a local South Sudanese, were seized along with a British UN employee and the Norwegian.
Williams rejected suggestions by the Sudanese army that the men were working in support of South Sudan in its "aggression" against the north.
"It's humanitarian work so the story of them being military advisers and this type of thing is completely and utterly nonsense and not true," Williams said.
"The abduction took place well within South Sudan territory," as they were travelling south towards their base in a mine-protected vehicle, he said.
"Then they grabbed them and drove back to Heglig with them where they then said they've arrested them in this disputed area while they weren't there at all."
The spokesman for Sudan's foreign ministry, Al-Obeid Meruh, told AFP that the diplomats' request for access has been transferred "to the authorised agency."
But he added: "Until now those people are under investigation."
The foreigners crossed illegally into Sudan and "we don't care if they are from the UN or not."
A British embassy spokeswoman said her mission was "urgently investigating the arrest of a British national in Sudan" and had requested consular access.
South Sudan broke away from Sudan in July last year after a peace deal ended one of Africa's longest civil wars, which killed about two million people between 1983 and 2005.
Tensions have risen over a series of unresolved issues including the border, the future of disputed territories and oil.
South Sudan's embassy estimates 350,000 ethnic Southerners remain in the north after an April 8 deadline for them to either formalise their status or leave Sudan.
Twelve thousand are camped south of Khartoum at the way-station of Kosti, awaiting a trip home by river barge.
But the governor of White Nile state which includes Kosti has branded them a security threat and given them a May 5 deadline to get out, official media reported on Sunday.
