The United States on Friday warned of a dangerous increase in tensions on the undemarcated border between Sudan and South Sudan after reports of clashes between the two sides.

Washington is "deeply concerned" by the reported incidents in disputed border areas between South Sudan's Upper Nile state and Sudan's Blue Nile, the US embassy in Khartoum said.

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

Hilde Johnson, who heads the United Nations mission in South Sudan, on Friday told reporters that authorities in South Sudan's Unity state, and the South's army, had reported Sudanese aerial bombing in Dar and Jau on Thursday.

African Union mediators have identified the locations as "a contested area," meaning the UN is not able to confirm what happened, she said.

On Wednesday, Sudan's army claimed "rebel forces" had infiltrated South Darfur state from South Sudan through the Central African Republic.

Military spokesman Sawarmi Khaled Saad, quoted by the official SUNA news agency, said the army "is monitoring closely the situation at the border with South Sudan."

The American embassy said it was "very concerned about the increase in negative rhetoric, which together with these reports of military clashes is leading to a dangerous increase in tension along the undemarcated border."

The embassy said it had no evidence of "an offensive buildup" on either side of the frontier.

"Our concern is that this increase in tension could lead to accidental confrontation that could quickly escalate," it added.

Sudan and South Sudan 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 agreements, 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.

"We strongly believe the tension underscores the importance of both parties agreeing to immediately and without conditions establish the Safe Demilitarised Border Zone (SDBZ)" along with a joint verification mechanism, the embassy said.

The United Nations had already told Sudan and South Sudan to activate the monitored SDBZ last May, under a Security Council resolution ordering an end to the earlier border clashes.

Khartoum accuses South Sudan of backing rebels in South Kordofan and Blue Nile states. This has been the major obstacle to implementing the September deals and resuming the flow of oil which is particularly vital to the South.

The Juba government stopped oil production more than a year ago, accusing Khartoum of theft during a row over how much the South should pay for shipping its oil through Sudanese pipelines for export.

South Sudan, which became independent in 2011, denies backing rebels on Sudanese soil. It says Khartoum supports insurgents on southern territory.

Diplomats and experts say Khartoum's concerns over border security are holding hostage billions of dollars in oil revenue for both economies.

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

Sudan's President Omar al-Bashir on Friday said his country will not succumb to international pressures seeking "to make Sudan change its position to the benefit of the South Sudanese government," SUNA reported.

"The agreements we signed in September will not be changed. We will not agree to change even a word of it," Bashir said. "We are committed to what we agreed."

He added that nobody can doubt Sudan's commitment to peace, SUNA said.