Much of the opposition boycotted the proceedings before voting started citing irregularities, and observers have already said the elections did not meet international standards.
Officials are still counting in many areas, but the few results they have announced point to a big win for the National Congress Party (NCP), led by President Omar Bashir.
The United States had already said the elections were neither free nor fair, and redoubled its criticism on Tuesday.
"Political rights and freedoms were circumscribed throughout the electoral process, there were reports of intimidation and threats of violence in South Sudan, ongoing conflict in Darfur did not permit an environment conducive to acceptable elections, and inadequacies in technical preparations for the vote resulted in serious irregularities," the White House said in a statement.
East Sudan's Beja Congress party, formally allied with the NCP, told Reuters it had managed to win only one seat in a state assembly in Red Sea state, but none in the national parliament.
The East is crucial to Sudan's oil-driven economy as it contains the only commercial port and miles of pipeline.
"We caught them (the NCP) emptying ballot boxes and they expelled our monitors from the voting centers during voting and counting," said Abdullah Moussa, a senior Beja Congress official in Port Sudan.
"We won this one (state assembly seat) only because it is a small area - one family and the young boys managed to guard many voting centers with small weapons at night," he said.
According to official results from another Red Sea state constituency, the NCP candidate won almost 18,000 votes compared to just 839 for the eastern party.
The NCP has repeatedly denied taking part in any irregularities.
The Beja Congress signed a peace deal with Khartoum in 2006, ending a lingering insurgency in the east, and its leader became a presidential assistant. But it has complained that the government has continued to neglect the region since the accord.
The Beja, made famous by author Rudyard Kipling as the "Fuzzy Wuzzies" because of their distinctive hairstyles, are one of the largest tribes in the region.
Taher Ali, a candidate from the Democratic Congress for East Sudan, told Reuters he had traveled to Khartoum to complain about numerous irregularities.
"In one voting center, the box with my votes had 600 ballot papers less than the other boxes and of those 485 were spoiled ... only 17 of the NCP's were spoiled," said Ali who was beaten to a seat in the national assembly by the NCP's current interior minister.
"Our people are furious - they want to go out onto the streets," he said. "We are trying to calm them." Bashir is the only sitting head of state wanted by the International Criminal Court for war crimes in Darfur and had hoped a victory would legitimize his government in defiance of the arrest warrant. He denies the charges.
The National Elections Commission had delayed announcing the results, citing technical problems, but said it was back on track and hoped to have the final presidential results by the end of the week.
The United States said on Monday Sudan's elections were neither free nor fair but it would deal with the victors to try to settle internal disputes before a 2011 referendum that could bring independence to southern Sudan.
On Tuesday the White House said it was committed to helping ensure that the referendum was conducted fairly.
