Violence has escalated along Sudan and South Sudan's border, further raising fears the countries are on brink of war, just nine months after they formally split.

The current president of the United Nations Security Council said the world body is gravely concerned about increasing confrontations along the two Sudans' border and deep into each other's territory.

The U.S. ambassador to the United Nations, Susan Rice, told reporters in New York Monday that the Security Council will meet to discuss the crisis, perhaps as early as Tuesday.

Rice condemned recent airstrikes by Sudan's armed forces in South Sudan, particularly one that struck a U.N. peacekeepers' facility on Monday.

South Sudan said Sudanese warplanes bombed parts of Unity State on Sunday, killing at least five people and wounding nine others.

The south also accused Sudan of bombing an oil field in the disputed border town of Heglig, which Juba's military seized from the north last week.

The U.S. envoy expressed concern about South Sudan's continued presence in Heglig, which is claimed by both the north and south.

Oil fields in Heglig produce about half of Sudan's total oil output, and South Sudan's presence has sparked threats of retaliation from Khartoum.

In a recent letter to the Security Council, South Sudan's acting deputy representative said it discovered last month that Sudan was building a new tie-in pipeline from Heglig oil fields in an attempt to siphon oil from Unity State in South Sudan.