South Sudan's government has rejected an accusation from Sudan that it supports rebels in a conflict-ridden Sudanese border state.

In a statement Wednesday, South Sudan's Ministry of Foreign Affairs said it “categorically denies” the accusation that it supports rebels in Sudan's Southern Kordofan state.

South Sudan said the conflict in the state is partly due to differences between Sudan's ruling party and the southern-allied SPLM party that followed last year's elections.

South Sudan also urged Sudan to implement provisions of a 2005 peace deal that ended Sudan's long north-south civil war, especially those addressing the rights of the people of Southern Kordofan.

Sudan made its accusation against South Sudan in a complaint submitted Tuesday to the U.N. Security Council.

Sudan's government is battling ethnic Nuba fighters in Southern Kordofan, who are seen as supporters of South Sudan, which declared independence from the north in July.

Nuba fighters supported the south during Sudan's 21-year war.

On Tuesday, two human rights groups said Sudan's army may have committed war crimes in Southern Kordofan. Amnesty International and Human Rights Watch said they have evidence of an “indiscriminate bombing campaign” by Sudanese forces.

In Washington, the U.S. State Department said it was deeply concerned by reports of aerial bombings of civilian areas and called on both sides to agree to abide by a two-week cease-fire in Southern Kordofan.

Sudanese President Omar al-Bashir called for the cease-fire last week. The fighting near the Sudan-South Sudan border has forced tens of thousands of Nuba from their homes.

Also Tuesday, the United Nations said Sudan's government has denied aid groups access to Southern Kordofan, leaving many people in a life-threatening situation.