Sudan has declared a state of emergency in areas bordering South Sudan, giving authorities there wide powers of arrest and detention.
A decree carried by the state media also included the creation of "special tribunals" to try suspects facing terror and customs offences.
The move, together with the arrest on Saturday of three foreigners and a South Sudanese in a disputed border area, are signs of spiking tensions along the disputed border, where clashes have raged in recent weeks.
The violence has brought the two nations, already at odds over demarcating the border and dividing oil revenue, to the brink of war.
South Sudan won independence last year as part of a peace deal that ended a long, bloody civil war.
A British man is among the three foreigners arrested on Saturday, the Foreign Office confirmed. The others are a Norwegian and a South African.
A Foreign Office spokesman said: "We are urgently investigating the arrest of a British national in Sudan. We immediately requested consular access and stand ready to provide further consular assistance."
Sudan's army spokesman said the men had military hardware and an armoured vehicle in their possession, Associated Press reported.
Colonel Sawarmi Khalid Saad said on state television that the four had military backgrounds and were carrying out military activities in Heglig.