He said the decision excluded the border states of South Kordofan and Blue Nile.
Last week the SPLM said that Yasir Arman, its presidential candidate, was withdrawing from the polls.
The government of Omar al-Bashir was accused this week of adopting repressive security measures and providing unequal access to state media by the opposition Umma party.
Call for reforms
Umma and several other opposition parties called on Friday for the government to implement crucial reforms within four days, including a revision of voter registration.
They said that they would not participate in the vote, which should be delayed until May if the reforms were not made.
Opposition groups have accused the government of only holding the election to re-elect al-Bashir to assist him in the face of an arrest warrant from the International Criminal Court (ICC).
The ICC, based in The Hague, Netherlands, has charged al-Bashir with war crimes for alleged attrocities in the conflict in the western Darfur region.
Reporting from Khartoum, the country's capital, on the SPLM's boycott decision, Al Jazeera's Mohammed Adow said: "It leaves the elections in tatters and also it means that its credibility is affected.
"President al-Bashir is one of the only few credible participants in the elections ... [and] the Umma party is now deciding whether to withdraw."
Earlier on Tuesday the national election commision said that the vote would go ahead, while about 50 people protested outside the commission's offices demanding "free and fair" elections.
Sunday's vote is the first general election to be held in the country for over two decades.
The Umma and the Democratic Unionist Party, now in the opposition, took first and second place respectively in the last elections in 1986.
Al-Bashir then took power in a military coup three years later.
Sudan has suffered two civil wars between the north and south of the country over the past five decades.
Fighting has also taken place between opposition groups and the government in the eastern Darfur region since 2003, killing about 300,000 people.