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.

In Washington Wednesday, the U.S State Department said it was concerned over allegations that South Sudan might be supporting rebels in Sudan.

It also reiterated its concern over reports that Sudan is carrying out bombings of civilian areas in the border region and called on both sides to stop hostilities.

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.

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. The fighting near the Sudan-South Sudan border has forced tens of thousands of Nuba from their homes.

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