Meanwhile, the rebel group in question, the Eastern Front, accused Sudan's military of terrorizing civilians in Red Sea state with constant overflights by fighter jets and other warplanes after charging last week that Khartoum had bombed civilian targets in the region.
The increasing verbal belligerence began with a statement from the Eritrean foreign ministry accusing Khartoum of committing "horrendous crimes" in the troubled western Darfur region and "atrocities" in eastern Sudan.
It ended with Sudan's foreign minister warning that the situation on the border could "explode" if Eritrea continues with what it claims is military support for the Eastern Front.
In its strongly worded statement, Eritrea scoffed at a Sudanese complaint to the United Nations about its alleged support for the rebels and denounced Khartoum for repressing minorities on its territory.
The Sudanese accusations "are either pretexts put forth in order to derail the entire peace process and renege from its commitments or deliberate diversion to foment problems in the region," the foreign ministry said.
"The horrendous crimes committed by the government in Khartoum in Darfur and the atrocities and injustices it has continued to perpetrate in the eastern and other underprivileged sections of the country in spite of the Naivasha Peace Agreement have remained a cause of concern to the government of Eritrea and the international community as a whole," it said.
That accord was signed in January between Khartoum and southern rebels to end 21 years of war and is hoped will serve as a framework for broader peace deals between the government and rebel groups in Darfur and the east.
Both the eastern and western groups claim their regions are being marginalized by the Arab-dominated government in Khartoum and Eritrea hosts offices for rebels from both regions.
Relations between Khartoum and Asmara have been tense for years with each side claiming the other supports rebel groups on the other's territory and their common border has been closed since 2002.
But the new row sent already strained ties plummeting with Sudanese Foreign Minister Mustafa Osman Ismail warning that the international community could expect a serious escalation in problems if Eritrea did not end its alleged support for the rebels.
"If Eritrea carries on with this behaviour, the international community should expect escalation," Ismail told reporters on the sidelines of a meeting of Islamic foreign ministers in Yemen.
"The international community... should expect also the situation in eastern Sudan and the borders (with Eritrea) to explode," he said.
Shortly before Ismail spoke, a senior official with the Eastern Front told AFP that Sudanese war planes were intentionally harrassing and frightening civilians in Red Sea state as a prelude to new aerial bombing.
Asmara-based Salah Barqueen said MiG-29s and Antonovs were overflying the Barka Valley "spreading terror and scaring civilians."
"If the flying doesn't stop, we will find ourselves compelled to respond with special treatment according to their aggression," he said. "The flying is an indication they will bomb again."
The Eastern Front, which launched its first offensive against government positions south of Port Sudan in Red Sea state on June 19, earlier accused the Sudanese air force of bombing civilians in a bid to stop their attacks.
Sudan immediately denied the charges but allowed that there were military operations in the area aimed at pursuing the rebels which included aerial reconnaissance.
The rebel charges have not been able to be independently confirmed due to the remoteness of the region about halfway between Port Sudan and the Eritrean border but Khartoum has been criticized in the past for bombing civilian targets in dealing with other insurgencies.
Barqueen was unable to provide any details about casualties sustained by civilians in last week's alleged bombing and could not say whether fighting between the rebels and government troops was continuing.