The British Foreign and Commonwealth Office updated its travel advisory for Sudan. The warning said it was advising against all travel to parts of the country near the border with Chad, South Sudan, Ethiopia and Eritrea.
A state of emergency was declared by Sudan in the border regions early this year because of the violence.
In Khartoum, it said it was wary about the threat posed to Westerners in the region.
"The FCO believes terrorists are planning to kidnap westerners in Sudan, probably in Khartoum," the advisory stated. "Take care in and around Khartoum, especially at night, and regularly change your patterns of travel."
Sudan and South Sudan this week recommitted to pledges made last year to stop supporting armed rebel groups in the region.
Rebel activity along their shared border has been a source of contention. Border conflicts and disputes over oil revenue have threatened to unravel the 2005 peace deal that secured South Sudan's independence in 2011.