"We don't have options in this respect. If they took the right to oppose the elections, we do have the same right to reject the referendum in the South."
Al-Bashir's National Congress Party (NCP) has ruled Sudan in a coalition with the SPLM since a peace deal that ended war between the two sides of Sudan in 2005.
The presidential and legislative elections on April 11 will be the country's first multiparty polls in 24 years, but the SPLM is calling for a boycott on the grounds that the vote will not be free and fair.
A scheduled meeting on Tuesday between the NCP and SPLM was abruptly cancelled.
"There was no agreement on the agenda to be raised to the presidency," Abdallah Masar, an adviser to al-Bashir, told the Reuters news agency late on Monday.
"There are differences over the elections - the NCP says the elections must happen on time."
Al-Bashir said no party was able to interfere with people's right to vote.
"I'll repeat for the second and third times that the elections represent the right of the Sudanese people for electing their deputies and electing their rulers," he said.
"The right for holding the elections was not accidental or a surprise. We've agreed on that in the January 2005 peace agreement in Nairobi.
"We'll not respond to any demand for postponing the elections for a month, two or three months ... No postponement for even a single day."
Yan Matthew, a spokesman for the SPLM, said the referendum would go ahead and that his party was only insisting on free and fair elections.
"The  agreement did not speak about the right of the partners to postpone the referendum in the South ... There are explicit items in this regard as in articles 122 and 123 of the peace agreement," Matthew told Al Jazeera.
"What has happened is an manifestation of anger [by the NCP] after they knew that the SPLM is the real threat to the power they had grabbed by force from the Sudanese people."
Last week, al-Bashir threatened to expel international observers who asked for any delay to the presidential and legislative polls.
The Carter Centre, the only international long-term observer mission in Sudan, had said a short delay may be necessary because of logistical problems, including hundreds of thousands of missing names on the electoral register.
The opposition wants the polls delayed until November, citing a continued conflict in Darfur and unresolved complaints of electoral irregularities.
The north-south civil war that began in 1983 claimed an estimated two million lives and destabilised much of east Africa.
When relations between the north-south partners hit a wall, the presidency usually meets and resolves the differences.
The decision to cancel Tuesday's meeting indicates how far apart their positions are less than two weeks ahead of the polls.