Another SPLA spokesman, Samson Kwaje, said one of the points of contention was the government's refusal to suspend Islamic law in the capital Khartoum during the transition period.
Islamic law is in effect in all government-controlled areas in the country.
Mediators had proposed an area of Khartoum to serve as a joint capital for six months which, according to Kwaje, was rejected by the government.
The SPLA spokesman also said the government wanted SPLA troops to be integrated into the national army, rejecting the idea that both sides maintain their own armies during the interim period.
Both delegations also hit a deadlock on the status of three regions claimed by both sides.
The SPLA is active in the disputed regional areas of Abyei, Southern Kordofan (also known as the Nuba Mountains) and the Blue Nile, and has since December claimed that it had the mandate from the people of those areas to represent them in the talks.
Khartoum insists those areas are not part of SPLA-controlled southern Sudan and that it controls most of the territories.
The SPLA said its representatives and the government delegation would meet again on 23 July to try to break the deadlock.
The SPLA has been calling for a religiously diverse south independent of the mainly Muslim north, but other issues at stake include oil and ethnicity.
The peace talks are sponsored by the regional Inter-governmental Authority on Development (IGAD), which groups Djibouti, Eritrea, Ethiopia, Kenya, Sudan, Uganda and nominally Somalia.
They were the final round of year-long negotiations to try to put an end to the conflict.
In July 2002, the two sides signed a protocol on two main issues - religion and the right for southerners to hold a referendum on independence.
But they have since struggled to agree on issues like sharing power and wealth, and how to structure the army.
The head of the opposition Sudanese Justice and Equality Movement, Khalil Ibrahim Mohammed, said on Friday his forces launched an attack against a government camp in the West Darfur state on the border with Chad. Mohammed added, his troops killed the commander of the camp and his deputy and seized ammunition before withdrawing.
Umm Durman radio reported that 13 government soldiers and 30 rebels were killed in the attack.