South Sudan has reached the 60% turnout needed to pass the referendum on secession from the north, the south's ruling party and ex-rebel group says.
"The 60% threshold has been achieved but we are asking for a 100% (turnout)," the SPLM's Anne Itto said.
She did not give exact figures, but said it was based on polling centre reports for the first three days of the week-long vote, which began on Sunday.
The poll was agreed as part of the 2005 deal to end the two-decade civil war.
The Sudan Peoples' Liberation Movement have been running the region since that peace agreement.
Official turnout figures - which along with the preliminary result, are not expected until the beginning of February - are the responsibility of the South Sudan Referendum Commission.
But the commission said on Wednesday it expected the vote, in which only southerners are taking part, to exceed the 60% mark.
UN patrols boosted
Nearly all of those registered to vote - almost four million people - live in the south.
People had stopped asking each other "how are you?" as a greeting and were instead asking "have you voted?", AP news agency reported Ms Itto as saying.
The BBC's Peter Martell in the main southern town of Juba says there were long queues at polling stations again on Wednesday, the fourth day of voting.
Trucks with loudspeakers have been criss-crossing the potholed dirt tracks of Juba urging voters to respond to SPLM's call for a "100% turnout", says our reporter.
But the shine has been taken off the jubilant mood by news of a deadly attack on a convoy of south Sudanese civilians near the north-south border returning home and clashes in disputed oil-rich region of Abyei earlier in the week, he adds.
Abyei was due to hold a separate referendum on whether to join north or south Sudan, but this has been postponed indefinitely because of disagreements over eligibility.
The semi-nomadic Arab Misseryia, viewed as allies of the north, say they want to vote in any referendum, but the Dinka Ngok, seen as loyal to the south, say that is not part of a 2005 peace deal.
The UN has boosted controls in Abyei, where an estimated 30 people have died in fighting since Friday. Each side blames the other for the violence.
Returning to Juba from a visit to Abyei, the SPLM's Secretary General Pagan Amum said the situation in the border region was now calm, although still tense.
"There are fears that Misseryia groups or militias may attack again," he told the BBC.
But he said the SPLM was ready to sit down for negotiations with the northern ruling National Congress Party to overcome the crisis.
Meanwhile the US state department has indicated it could remove Sudan from its list of state sponsors of terrorism if the north recognises the outcome of the poll.
"It is a process that takes some time, but by beginning the process in the wake of the referendum, the hope is if they meet all the conditions, it can be done by July," US diplomat Princeton Lyman told AFP news agency.
Southern Sudan would become Africa's 54th nation on 9 July 2011 if the referendum is passed.
North and south Sudan have suffered decades of conflicts driven by religious and ethnic divides, with an estimated 1.5 million people killed in the civil war.