The SPLM said it had asked for polling to be extended from three to seven days.
'Mix-up of ballots'
"There have been a lot of irregularities that we have noticed," Samson Kwaje, the campaign manager for Kiir, the SPLM leader, said.
"Today was a wasted day. We are seriously sending a protest to the NEC [National election Commission]."
The NEC acknowledged there had been "mistakes" in distributing ballot papers in some areas but made no comment on the possibility of extending voting.
Al Jazeera's Mohammed Adow, reporting from Khartoum, the capital, said the problems continued on the second day of voting.
"The election commission ... say they are working to try and rectify those problems. In some areas - like in the district of Barber, in the White Nile state, in the north - voting has been postponed for up to two months," he said.
"Most of the problems ... are [to do with] a mix-up of ballot papers, and also symbols of candidates and political parties being swapped between the different candidates who are contesting these elections."
Our correspondent said there has been "so much anger and acrimony" and that some independent candidates had threatened to pull out of the election.
The confusion in voting has been compounded by a high level of illiteracy among the electorate who have to cast multiple ballots for for presidential and parliamentary candidates.
The election had already been mired in controversy after key candidates withdrew ahead of polling day citing fears of fraud.
The SPLM pulled out Yasser Arman, its presidential candidate, who many thought would be the main challenger of Omar al-Bashir, the incumbent president seeking re-election after being in power for almost 21 years.
Sadiq al-Mahdi, Sudan's former prime minister from the northern opposition Umma party, also withdrew citing possible fraud.
The opposition parties have accused the National Congress Party of al-Bashir of plotting to fake an election victory, particularly after the contract for ballot papers went to a state-owned printer.
The election comes less than a year before Sudan holds a referendum in January 2011 on the independence for the oil-producing south, whose government is in a coalition with al-Bashir's government after a peace agreement was signed in 2005 with the SPLM to end a decades-long war in the south.
The results are widely expected to return to power al-Bashir, who is facing an arrest warrant from the International Criminal Court (ICC) for alleged war crimes in the western Darfur region.
In Darfur, where an estimated 2.7 miilion people have been displaced by a seven-year conflict between the government and ethnic monority rebel groups, international peacekeepers reported no violence.
"So far the situation is calm," one peacekeeper with the joint UN-African Union mission told the AFP news agency.
But Mohamed Vall, Al Jazeera's correspondent in the region, said there were complaints that many ballot papers were delivered to the wrong places.
European Union monitors pulled out of Darfur before polling day citing concerns about security in the region.
However, Darfur rebel groups, which control parts of the vast region and boycotted the elections, have not stated any intention to disrupt voting.