"President Bashir refused to personally receive the letter that Riek Mashar, vice-president in the southern semi-autonomous government, was to deliver," Dang Goj, SPLM spokesman told the AFP news agency.
"For us this is a negative signal, an escalation and negligence of our demands."
The SPLM withdrew its ministers from the national coalition government on Thursday, saying it had failed to follow through on a peace deal signed in 2005.
The withdrawal sparked a wave of international concern, with Ban Ki-moon, the UN secretary-general joining the US state department in urging both sides to keep the Comprehensive Peace Agreement between Sudan's government and the SPLM alive.
Commentators have said a collapse of the peace process would have a devastating impact on security across Sudan, including its war-torn western Darfur region.
The pullout raised fears of complicating peace talks planned for October 27 between Khartoum and Darfur rebels, who accuse the military and allied militia of increasing attacks after four years of civil war.
|"President Bashir refused to personally receive the letter that Riak Mashar, vice-president in the southern semi-autonomous government, was to deliver"|
Dang Goj, SPLM spokesman
The exact contents of the letter were unknown, but the SPLM's demands are focused on getting Khartoum's troops out of the south, resolving the fate of the central oil-rich province of Abiye and getting Bashir to allow southern ministers to be reshuffled.
But Bashir's National Congress party has accused the SPLM of failing to implement the Comprehensive Peace Agreement which ended 21 years of war between the north and south that left at least two million people dead and displaced millions more.
The United Nations mission in Sudan reiterated its readiness to help the north and south settle their differences after Ban Ki-moon expressed his concern at the crisis.
"The UN is encouraged by the contacts and the consultations to be taking place at the highest level between the NCP and the SPLM," Radia Achouri, the Unmis spokeswoman, said.
"The UN preference is for the two partners to resolve the issue through consultation and dialogue," Achouri said, adding that the UN was not mediating but "was ready to offer its good offices to assist the parties if requested."
Around 10,000 UN peacekeepers are deployed in southern Sudan to observe security arrangements, including implementation of the peace agreement.