The South Sudanese leader has urged his people to forgive the north for killings during a civil war that lasted more than 20 years.
Salva Kiir made the appeal from the pulpit of a Catholic Cathedral in Juba.
Early results from Southern Sudan's referendum indicate the region has voted overwhelmingly to split from the north and form a new country.
Full results of the poll are not due until next month, but the region is widely expected to choose to secede.
"For our deceased brothers and sisters, particularly those who have fallen during the time of struggle, may God bless them with eternal peace," Mr Kiir said on Sunday, in his first public address since the vote.
"And may we, like Jesus Christ on the cross, forgive those who have forcefully caused their deaths."
An estimated two million people died in the war between the mainly Muslim north and the largely Christian south.
The referendum was part of a peace agreement signed with north Sudan in 2005.
Correspondents say there has been little doubt that Southern Sudan would opt for secession.
Polling stations opened on 9 January and were officially closed on Saturday evening.
A minimum 60% turnout was required for the vote to be considered valid, a target which had easily been passed by the middle of the week.
The chairman of the Southern Sudanese Referendum Commission, Mohamed Ibrahim Khalil, has said more than 80% of eligible voters in the south had cast their ballots, along with 53% in the north and 91% of voters living in the eight other countries hosting polling stations.
He said the referendum would be considered "a good result by any international standard".
The Associated Press reported a 95% turnout at 10 sites in Juba, which would be the capital of a future Southern Sudan. A sample suggested that 96% had voted in favour of secession.
Southern Sudanese people living in Europe have already voted 97% in favour of a new state.
Southern Sudanese people living in Australia have been given extra time to cast their votes where severe flooding has hampered the process.
International observers in Southern Sudan have been almost universally optimistic, saying the balloting process has been free and fair.
The BBC's Peter Martell in Juba says that has come as massive relief to the south, for whom this vote means so much.
The process was marred, however, by a deadly attack on a convoy of south Sudanese civilians earlier this week.
US President Barack Obama and UN Secretary General Ban Ki-moon have both praised the vote.
Sudan's President Omar al-Bashir has promised to accept the results of the poll either way, even if it meant the partition of Africa's largest nation.
"The referendum took place in an atmosphere of calm with a great degree of freedom and fairness," Rabie Abdul Ati, a senior official in Mr Bashir's National Congress Party (NCP), told the AFP news agency.
"It is very clear that the party will accept the result whether it be for unity or secession."
For when they shall say, Peace and safety; then sudden destruction cometh upon them, as travail upon a woman with child; and they shall not escape.
(I. Thessalonians 5:3 KJV)
(I. Thessalonians 5:3 KJV)