Sudan's Minister of Defense Abdel-Rahim Mohamed Hussein recently said that any rebel activity in Sudan's South Kordofan state could cancel the agreements. Sudan is battling the rebel SPLM-North, which until South Sudan's secession was linked to the south's ruling party — the SPLA. The south has said it is not supporting the SPLM-North.
The cancellation of the presidential summit will set north-south relations back, said Aly Verjee, an analyst for the Rift Valley Institute.
"The new fighting unfortunately trumps progress made in recent negotiations. It is unsurprising that talks have been canceled given those events," he said.
Marial said South Sudan is still committed to the presidential summit.
"Our invitation still stands as it is. These are forces within the (ruling) NCP party which don't want this process to continue," he said.
The U.N. refugee agency said Tuesday that it fears for the safety of refugees who have fled the fighting in South Sudan after the violence flared up in recent days. Spokeswoman Melissa Fleming said more than 16,000 people who have fled the Nuba mountains in Sudan are currently living in South Sudan's Yida settlement.
She said the agency wants to move the refugees away from the border where the fighting is taking place.
In total, more than 105,000 Sudanese have fled to South Sudan and 30,000 have fled to Ethiopia.
Associated Press writers Mohamed Osman in Khartoum, Sudan and Frank Jordans in Geneva contributed to this report.