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.

"We are ready to teach you another lesson," Bashir said.

South Sudan President Salva Kiir responded last week, saying al-Bashir's accusation are only to justify "his pending invasion." Kiir said South Sudan is committed to peace but allow its sovereignty to be violated.

Last week U.S. and other international officials said Sudanese military aircraft twice flew into South Sudan territory and dropped bombs. In the second attack two bombs landed in a refugee camp. There were no casualties.

The U.S. demanded that Sudan halt aerial bombardments immediately.

"This is a moment where both sides need to show maximum restraint," said Susan Rice, the U.S. ambassador to the U.N. "In the first instance, the government of Sudan needs to halt all offensive actions against the south. Immediately. And the south needs to have the wisdom and restraint not to take the bait and not to respond in kind."

U.N. Secretary-General Ban Ki-moon called on the governments of Sudan and South Sudan to refrain from using force.

Ban expressed "deep concern" Monday at the escalating rhetoric between the two governments and called on them "to exercise restraint in managing border tensions," U.N. spokesman Martin Nesirky said.

The U.N. chief said outstanding issues in the 2005 peace agreement that ended the north-south civil war can only be settled through negotiations.

U.N. peacekeeping chief Herve Ladsous and Hilde Johnson, head of the new U.N. mission in South Sudan, echoed Ban's comments on Tuesday as they urged both sides to tone down their accusations.

The claims about alleged cross-border incursions are "extremely worrying," Ladsous told the Security Council during a briefing in New York. "We are concerned by the hate and rhetoric on both sides," Johnson told council members by videoconference call from South Sudan.

The aid group Oxfam said over the weekend it was pulling out 22 staff members _ mainly engineers and health workers _ from South Sudan's Upper Nile state after the staff reported a bombing and heavy artillery on Friday. The staff witnessed planes overhead and a build-up of South Sudan troops, Oxfam said.

"New bombing raids and a build-up of troops along the border of Sudan and South Sudan over the past few days threaten to escalate what is already a significant humanitarian crisis," it said, adding: "Thousands of refugees are still coming across the border ... they have fled attacks and walked for days to reach a place they thought would be safe but instead they are now facing more violence."

The World Food Program also suspended activities in the Yida refugee camp _ home to more than 20,000 refugees _ after two bombs from Sudanese aircraft fell in the camp and three outside of it.

Lise Grande, the U.N. humanitarian coordinator in South Sudan, said the attack "put innocent civilians at extreme risk."

A new Sudan rebel group calling itself the Sudan Revolutionary Front has emerged, adding to the dizzying array of political and military groups involved in an ethnic, economic and territorial conflict between the two countries.

The Sudan Revolutionary Front says its aim is to overthrow the Sudan's ruling National Congress Party through all means, including violence. The group consists of the Sudan People's Liberation Movement-North, the Justice and Equality Movement, and two factions of the Sudan Liberation Movement/Army.

The group said it believes Sudan's government is at a weak point economically, politically and militarily.

"The regime is imploding and will vanish, like other corrupt regimes around us that have come to rely on repression to retain power," the group said. "It has humiliated our people and dismembered our homeland. Should its rule continue, it would lead to further division in Sudan."

Eric Reeves, a Sudan expert at Smith College in Northampton, Massachusetts,said the group could force Khartoum to face the "daunting prospect of fighting resource-draining wars on several fronts, with the likely shut-down of oil extraction and transport from the south."

"It will take efforts not in sight to avoid a return to war," Reeves said.

Khartoum's National Congress Party said the Sudan Revolutionary Front is planning to carry out acts of sabotage to lead Sudan into a crisis. The official news agency quoted a ruling party spokesman, Yassir Yusuf, as saying that the government of South Sudan should "distance itself and lift its hand to stop providing assistance to rebel movements in Sudan."

For months Sudan has been attacking what it calls rebel groups in the states of Blue Nile and South Kordofan. An ethnic group called the Nuba live in South Kordofan, and they appear to be on their own. Not part of the black southerners that now make up South Sudan, they are also not Arabs of the north. Thousands have fled to live in caves the past several months as military jets from the north have dropped bombs.

Though oil is a large component in the building conflict, Reeves said, the Nuba have no interest in oil. He recalled a meeting he attended with the Nuba almost eight years ago.

"It was clear to me in 2003 that the Nuba would fight to the death to save their lands," he said.

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Associated Press reporter Mohammed Osman in Khartoum, Sudan, contributed to this report.