The militants had threatened to execute him on Friday if they were not given US3 million (about R32.5m) in exchange for his safe return.
“Pierre is alive,” foundation head Imtiaz Sooliman said in a statement.
“We have achieved a stay-in-execution for now. We have been granted a three-week extension [to raise the ransom].”
Sooliman said the militants had informed them that Pierre Korkie was not in good health.
After no communication from the kidnappers for almost three days, Gift of the Givers contacted them on Friday night and arranged to meet with them, said Sooliman.
Anas al-Hamati, an organisation representative based in Yemen met with the kidnappers on Saturday at 4am.
“The meeting was cordial and decent. We [the foundation] agreed to pursue further discussions in the days to come,” said Sooliman.
Korkie and his wife Yolande were kidnapped in the city of Taiz in Yemen in May last year.
After extensive negotiations, Yolande Korkie was released without a ransom and returned to the country on Monday.
Speaking at a media briefing in Johannesburg on Thursday, a frail Yolande begged Al-Qaeda to release her husband.
“Al-Qaeda, I ask to address you. Thank you for releasing me and giving me back to our children, treating us with kindness and respect, and bringing my husband medicine… I’m asking you to release my husband,” she said.
“We are asking you to show mercy, to please show tolerance.”
The couple have been married for 20 years. At the time of the kidnapping, Korkie was a teacher in Yemen, while his wife did relief work in hospitals.
It was believed that Al-Qaeda kidnapped the couple thinking they were US citizens.
Meanwhile, Deputy Minister of International Relations Ebrahim Ebrahim was scheduled to travel to Yemen on Saturday to discuss Korkie’s kidnapping with the Yemeni government and interested parties.
Ebrahim’s department said on Friday they would not be involved in the ransom talks.
“Our policy is well-known to the public that government does not negotiate or pay ransom to kidnappers,” said department spokesman Nelson Kgwete.
“We are involved in efforts to free him through diplomatic channels.”