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Poland says racism was not a factor in its decision to refuse entry to South African presidential guards and media for almost 24 hours.
About 120 people were stuck on the aircraft at Warsaw's Chopin airport.
They were on their way to a peace summit in Ukraine, but Poland's actions have left President Cyril Ramaphosa 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.
He and Poland's Border Guard say the South African security officers did not have the correct paperwork for their weapons.
"Members of the delegation had weapons for which they did not have permission to bring in, but they could leave the plane themselves," the agency wrote on Twitter.
What started as an impasse on Thursday afternoon has escalated into a diplomatic row.
A spokesman for South Africa's president says the row is "regrettable". Efforts are now being made to ensure those on the aircraft can proceed "to cover at least the Russian leg" of the trip, spokesman Vincent Magwenya adds.
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 is News24 journalist Pieter Du Toit, who praised South Africa Airlines staff for being "quite brilliant in supporting everyone on the plane".