(CNN) -- The Sudanese president has vowed to "never give up" a disputed oil-rich region that has escalated tensions with South Sudan and sparked fears of the two neighbors' return to war.
Clashes between the two nations soared in the past week after South Sudan declared the disputed Heglig region is under its control.
Sudan also claims ownership and has lodged complaints with the United Nations and the African Union, urging them to pressure South Sudan to withdraw troops from its territory.
The United States on Thursday called for both sides to stop the hostilities.
"We condemn South Sudan's military involvement in the attack on and seizure of Heglig, an act which goes beyond self-defense and has increased tensions between Sudan and South Sudan to dangerous levels," State Department spokeswoman Victoria Nuland said. "We also condemn the continued aerial bombardment in South Sudan by the Sudanese Armed Forces."
U.N. Secretary-General Ban Ki-moon urged both countries to return to the negotiating table.
"The last thing the people of these two countries need is another war -- a war that could claim countless lives, destroy hope and ruin the prospects of peace and stability and prosperity of all Sudanese people," he said.
China, which has invested heavily Sudan's oil industry, also argued for calm.
"China again calls for the two countries to immediately stop hostility and respect each other's sovereignty," Liu Weiming, a spokesman for the Chinese Ministry of Foreign Affairs, said at a regular news briefing Thursday.
During a rally broadcast on state media, Sudanese President Omar al-Bashir said, "We will never give up an inch of our land. And we have said it before, whoever extends his hand toward Sudan, we will cut it off."
The international community has urged Sudan and South Sudan to return to the table amid intensified tensions. South Sudan split from its neighbor in July under the terms of a 2005 peace agreement that ended decades of a civil war.
During the defiant speech, the Sudanese leader told citizens that "Heglig is in Kordofan," referring to a border state owned by the nation.
"We will punish them ... and it will be the last lesson for them," he said. "If they do not understand, we will make them get it by force. We extended our hand before for peace and unity. But they deceived us. Heglig is the start."
South Sudan did not immediately respond to the latest speech, but a military official vowed to retain a grip on the region a day earlier.
"We will hold this position," said Maj. Gen. Mangar Buong, a deputy commander for the South Sudanese military.
Princeton Lyman, the U.S. Special Envoy for Sudan and South Sudan, has been in both countries recently, holding meetings with government officials.
There is "an enormous amount of very emotional, very powerful rhetoric coming from here in Khartoum raising the stakes in many ways and that's worrisome in and of itself," he said on a conference call from Khartoum on Thursday.
But he said that based on the discussions he'd had in both Khartoum and Juba, "I can say with confidence that virtually everyone I have talked to has said, 'Look, we don't want to go to all out war with the other, we need to find a way out.' "
Tensions run deep between the two nations, which have outstanding issues despite their divorce last year.
Unresolved issues include status of citizens, how much the landlocked South should pay to transport its oil through Sudan and the division of national debt, among others. The fate of disputed border areas is also a point of contention.
As long-simmering tensions soar, rights group are warning of deteriorating humanitarian conditions.
"The deteriorating situation right now is making the overall humanitarian issues very challenging," said Alex Neve, secretary-general of Amnesty International Canada.
Neve, who is in the South Sudan capital of Juba, said supply lines at refugee camps have been cut off and failure to get key supplies before the rains will lead to a humanitarian crisis.
In addition, there are reports of human rights violations.
"The refugees coming in across the border have consistent stories of aerial bombardments and ground attacks" from Sudanese soldiers, he said.
CNN's Amir Ahmed, David McKenzie, Faith Karimi and Jamie Crawford contributed to this report.