KHARTOUM: Rebels wounded during fresh fighting in Sudan's Blue Nile state have retreated to South Sudan, the army said on Monday, after Washington warned of a dangerous increase in tensions on the undemarcated border.

The army statement followed claims by rebels of the Sudan People's Liberation Movement-North (SPLM-N) that a government offensive in Blue Nile had forced thousands to flee.

Sudan's army spokesman, quoted by the official SUNA news agency, said the army had "liberated" an area in southwestern Blue Nile, killing and wounding dozens of insurgents.

"Those injured have been taken to South Sudan," said the spokesman, Sawarmi Khaled Saad. "The rebels withdrew towards South Sudan."

Saad added that "a number" of government troops were killed and wounded, but he gave no figures.

The United States on Friday said it was "deeply concerned" by reports of clashes between Sudan and South Sudan in disputed border areas between Blue Nile and South Sudan's Upper Nile state.

These included "reports of Sudanese helicopters crossing into South Sudan and the artillery bombardment by Sudanese armed forces of South Sudanese troops," the American embassy in Khartoum said.

The embassy added that it was "very concerned about the increase in negative rhetoric."

Yasir Arman, secretary general of the SPLM-N, in a statement on Sunday accused the armed forces of "a military dry season campaign" which began on Thursday in an area about 20 kilometres (12 miles) southwest of Blue Nile's El Kurmuk town.

"The fighting has gone on for the last three days with heavy aerial bombardment from Sudan's air force", forcing 8,000 people to flee towards the borders of South Sudan and Ethiopia, Arman said.

Access to Blue Nile is restricted, making verification of claims difficult.

Figures from the humanitarian wing of the rebels along with data from the government's aid agency indicate that more than one million people have been affected by unrest in Blue Nile and South Kordofan states.

The SPLM-N, which has been fighting in the two areas since 2011, belongs to a Sudanese rebel alliance seeking to topple the Islamist Khartoum regime to implement greater "democracy" and respect for diversity.

Sudan and South Sudan, which became independent two years ago, fought along their frontier last March and April.

In September they hailed an end to conflict by signing security and economic agreements, but these have not been implemented.

The deals, reached with the help of African Union mediation, called for a resumption of oil flows between the two countries and creation of a demilitarised border buffer zone.

The government accuses South Sudan of backing rebels in South Kordofan and Blue Nile, which has been the major obstacle to putting the September deals into effect.

Diplomats and experts had also expressed concern that tensions were escalating and said there is no immediate hope of a resolution to the dispute.

The United Nations and the African Union have for months called on the SPLM-N and Khartoum to reach a negotiated settlement, but the latest deadline for talks passed unnoticed last Friday.