"Our forces destroyed three big camps and other smaller stations," said Salah Barqueen, secretary for legal affairs of the Beja Congress, which merged with the Rashaida Free Lions in February to form the Eastern Front.
The fighting started when the rebels launched a major offensive for control of the Red Sea town of Tokar, some 120 km south of Port Sudan.
In a statement issued on Monday, the Sudanese army claimed that it had dealt with the offensive and was in complete control of the area, the official Sudanese news agency reported.
Barqueen, however, refuted the government claims. By Tuesday, he said, the rebels had captured 20 government soldiers and significant quantities of weapons and ammunition.
Speaking at the Beja Congress offices in the Eritrean capital, Asmara, he told IRIN that the attack involved both eastern rebels and those from the Justice and Equality Movement in the western Sudanese region of Darfur.
Analysts said the clashes were a setback to progress made in Cairo on Saturday, when Ali Osman Taha, Sudan's first vice-president, and Mohamed Osman al-Mirghani, leader of the National Democratic Alliance (NDA), signed a peace deal between the government and the NDA.
The agreement was intended to end 16 years of hostilities between Khartoum and the country's largest coalition of opposition groups.
The Beja Congress and Rashaida Free Lions are both officially members of the NDA but pulled out of the reconciliation talks in Cairo. The rebels have controlled a small area of territory across the border from Eritrea since the late 1990s, but both the Beja Congress and the Eritrean government have denied any Eritrean military support for the rebels.
Barqueen said like other Sudanese opposition parties, the Beja Congress was allowed to move freely in and out of Eritrea, to access the media, and to keep an office in Asmara.
"We will not put our arms down until we achieve our aims," he said, adding that 90 percent of Beja rebel arms had been captured from Sudanese government forces. The rebels, he explained, were fighting so that eastern Sudan could share in the country’s power and wealth.
"We want fair and just relations between those with power and wealth and those who live on the margins," Barqueen said. "Unless I am part of this justice and equality, I do not want to be part of this country."
Sudanese President Omar Hassan el-Bashir said at the Cairo peace-agreement signing on Saturday: "Negotiations are underway in [the Nigerian capital] Abuja, and we all have hopes that the efforts made in Abuja will be crowned with an agreement that restores security, peace and tranquillity to our people in Darfur.
"Efforts also continue to reach, with God's will, an agreement with some of the sons of the east so that Sudan becomes united and we start a new stage in the history of Sudan," he added.
The leader of the southern Sudan People's Liberation Movement/Army (SPLM/A), John Garang, said: "By rallying the Sudanese together and now with the comprehensive peace agreement we signed, we can have a true democratic change in our country and we can have a true new Sudanese unified state, a new Sudan."
The NDA, consisting of a dozen or so largely northern political parties, trade union representatives and the SPLM/A, has opposed Bashir's government - both politically and militarily - since he came to power in a military coup in 1989.
Under the reconciliation agreement, the NDA would be incorporated into the power-sharing government agreed upon under the administration's peace deal with the SPLM/A signed in January.
The eastern rebels have clashed intermittently with government forces in eastern Sudan since 1996, Beja sources said, but tension has risen in recent months.
In January, Sudanese government forces opened fire on Beja demonstrators in Port Sudan, killing more than 20 people. The rebels said they would not talk to the government unless those responsible were brought to justice and 18 of their leaders, imprisoned following the events in Port Sudan, were released.
In May, the Sudanese government promised US $88 million in development aid for the area, but Barqueen claimed the announcement was an attempt to divert international attention away from their crimes in Port Sudan.
The rebels subsequently kidnapped three Sudanese officials who were travelling in government-controlled territory.
Humanitarian conditions in the rebel-controlled area of eastern Sudan are difficult, according relief workers.
Fergus Thomas, programme coordinator for the International Rescue Committee in northeast Sudan, said in April: "It is the most underserved, most remote area that I have ever worked in, with huge humanitarian needs."