Poland says racism was not a factor in its decision to refuse entry to South African presidential guards and media for more than 24 hours.
The stand-off happened at Warsaw’s Chopin airport. The aircraft will now be held there until Sunday, an airport spokesman told the BBC.
About 120 people were stuck on the plane, who were all on their way to a peace summit in Ukraine.
Some of the passengers are now disembarking and going to a hotel.
Poland’s actions have left President Cyril Ramaphosa, who travelled separately to Ukraine, without some of his security detail.
This prompted a furious reaction from Mr Ramaphosa’s head of security, Maj Gen Wally Rhoode.
“They are delaying us, they are putting the life of our president in jeopardy,” he told journalists. “We could have been in Kyiv by now and this is all they are doing. I want you guys to see how racist they are.”
But Poland has dismissed this outright.
“Accusations against Poland of racism are being circulated in this case. This is nonsense,” says the director of the National Security Department and spokesman for Poland’s Minister-Special Services Coordinator, Stanisław Żaryn.
Warsaw Chopin airport spokesman Piotr Rudzki told the BBC the South African security guards did not have the necessary permits for their weapons.
“We cannot let passengers with illegal firearms into the EU,” he said.
Mr Rudzki added that they were told they could disembark if they left their weapons on the plane but they refused.
“The firearms… were not going to be confiscated as some reports in South Africa have said,” he added.
What started as an impasse on Thursday afternoon has escalated into a diplomatic row.
A spokesman for South Africa’s president said the row was “regrettable”. Vincent Magwenya had said efforts were being made to ensure those on the aircraft can proceed “to cover at least the Russian leg” of the trip. But according to Mr Rudzki, this is no longer an option.
Despite the events in Warsaw, Mr Magwenya says President Ramaphosa arrived safely in Ukraine’s capital Kyiv safely by train from Poland, along with other African heads of state who are visiting the country to promote dialogue with Russia.
“I would like to assure all South Africans that there has been no compromise whatsoever to the president’s safety as a result of the impasse that involved the charter flight with the presidential protection services team and the media,” he says in the video posted on Twitter.
During the African delegation’s visit to Ukraine on Friday, the military said it had come under missile attack and returned fire – shooting down more than a dozen projectiles.
Ukrainian Foreign Minister Dmytro Kuleba said the message was clear: “Russian missiles are a message to Africa: Russia wants more war, not peace.”
Both Russia and Ukraine have sought to deepen their influence in African nations in recent months.
South Africa says it does not want to take sides in the conflict but the US has accused it of supplying weapons to Russia, which it has denied.
The delegation from South Africa, Egypt, Senegal, Congo-Brazzaville, Comoros, Zambia, and Uganda is meeting President Volodymyr Zelensky on Friday and President Vladimir Putin on Saturday.
One of those on the plane in the Polish capital was News24 journalist Pieter Du Toit, who praised South Africa Airlines staff for being “quite brilliant in supporting everyone on the plane”.
A few hours before he was allowed to disembark, he did however say that supplies were running thin, and joked that the passengers were deciding how to chop up the last remaining chip from a Burger King order delivered the night before by the South African embassy.
