The vote has been boycotted by the main opposition parties, many of whom have been called for it to be scrapped entirely, while those opposition groups that have taken part have complained that the process is flawed and riddled with irregularities.
The former southern rebel Sudan People's Liberation Movement (SPLM), which had requested a four-day extension, said it would press for more days due to the delays in deliveries of material and ballot papers.
It added that many people had to search for hours to find voting centres.
"I appreciate the effort of the NEC. We had requested for four more days," Samson Kwaje, the campaign manager for Salva Kiir, the leader of southern Sudan, told reporters.
With two days we are quite satisfied, but we are still thinking it is not enough. We are going to press for more."
Jimmy Carter, the former US president who is visiting Sudan as an election monitor, said there was "not much doubt" polling would be extended after a chaotic start on Sunday prompted cries of foul play and forced officials to admit "mistakes."
"There were some serious problems with the election process in some voting places where lists have been very difficult to find your names, where voters have difficulty finding their names," Carter told reporters in Juba, the capital of south Sudan.
"In some cases, wrong ballots were sent to other places in southern Sudan."
Mariam al-Mahdi, a spokeswoman for the opposition Umma party, told reporters the vote had become "a very expensive problem".
Al Jazeera's Mohammed Adow reports on Sudan's decision to extend the polls
"We were better off without elections. It's nonsensical," she said. "There is no need for any extension because the whole process has collapsed."
The poll is the first multi-party election held in Sudan since 1986.
The vote is part of a 2005 peace deal that ended 21 years of a north-south civil war, intended to install a democratically elected government for the impoverished country and prepare for a referendum next year over the status of the south.
However, opposition parties have criticised the elections saying the process is flawed and heavily controlled by the ruling National Congress Party headed by Sudan's president, Omar al-Bashir.
The US is one of the main sponsors of the peace deal between the north and south and has been heavily involved in the two regions to ensure the elections and the subsequent referendum, which the south wants to use to gain independence, takes place.
"With voting under way in Sudan, I think we're satisfied with the start of the process," PJ Crowley, the US state department spokesman, told a news briefing, acknowledging there had been "challenges" in preparing for the election.
|The polls have so far been marked by confusion and allegations of fraud [Reuters]
A group of opposition parties who boycotted the voting have accused the US of backing the polls in exchange for the central government allowing the referendum, and the south's eventual secession, to happen.
Mariam Sadiq, a senior member of the opposition Umma party, said there had been a deal to separate the north from the south by ensuring that al-Bashir wins re-election.
Al-Bashir's victory "is meant to separate the south by electing an agreed upon political figure," Sadiq told the The Associated Press news agency.
Farouq Abu Issa, a spokesman for the opposition groups, told a news conference in the Sudanese capital Khartoum that Washington is "seeking to manage the elections in Sudan they way they managed them in Iraq".
Al-Bashir, who is facing an arrest warrant from the International Criminal Court (ICC) for alleged war crimes in the western Darfur region, is widely expected to be returned to power following the elections.