NAIROBI, Kenya — The presidents of Sudan and the new nation of South Sudan are both predicting the possibility of a new war in an oil-rich region that has seen a spike in cross-border attacks.

Troop build-ups are being reported on both sides of the Sudan-South Sudan border, the world’s newest international boundary, and rebels in Sudan announced a new alliance with the aim of overthrowing their own government, which is seated in the capital, Khartoum.

The U.S. is pleading for cooler heads to prevail, even as aid workers are withdrawing from the region after two bombing runs into South Sudan by Sudan, its northern neighbor, last week.

After two long wars that spanned decades, South Sudan formally declared independence from Sudan in July following a successful independence referendum in January that was guaranteed in a 2005 peace deal. The world celebrated the peaceful break-up of Sudan. But big disputes that have long lurked in the background are now festering, and flaring into violence.

An agreement to split the region’s oil revenues was never reached. The borders were never fully demarcated. And perhaps most important, the break-up left two large groups of people in Sudan’s south in the lurch, groups that Sudan has labeled rebels and that Khartoum’s military has been attacking for months.

In addition, the Khartoum government is facing a financial crisis due to the loss of oil revenue and rising food prices, said John Prendergast, the co-founder of the U.S.-based Enough Project, which closely monitors Sudan.

“Each spark heightens the possibility of all-out war, and the sparks are occurring with more frequency now,” Prendergast said Monday.

Sudan President Omar al-Bashir accuses the south of arming what he calls rebels in Sudan. He said this month that if the south wants to return to war, his army is prepared, as he ticked off recent clashes he said the north won.