A near-riot erupted on an aeroplane over South Africa as football fans rushed towards the cockpit to protest at missing last night's World Cup semifinal between Germany and Spain, witnesses have claimed.

The fans were among hundreds of angry ticket holders whose flights were delayed or turned back because Durban's new King Shaka international airport was full. Some complained that priority had been given to private jets used by celebrity spectators such as Paris Hilton and Leonardo DiCaprio.

The atmosphere became fraught on a flight from Cape Town to Durban when the captain announced it was being redirected to Johannesburg, passenger Jay Moodley told the Mercury newspaper. "There was almost a riot on the plane and about 10 foreigners rushed towards the cockpit," he was quoted as saying. "The captain told them that they would be arrested if they did not sit down. Things were very tense."

About 20 minutes later it was announced that a slot at King Shaka airport had become available and the plane would land at 8.50pm – two hours late.

Moodley added: "People rushed off the plane and were trying to make it to the stadium in time for the second half. There was a huge anticlimax when we landed and people were giving Durban the thumbs-down."

In the chaos two planes were forced to turn back, while three others were allowed to land after severe delays. Passengers were given a police escort to the game but still missed most or all of it. Attendance at the Moses Mabhida stadium was 1,800 below capacity for Spain's 1-0 victory.

Today many fans, some of whom spent thousands of pounds to be at the World Cup, said they were considering suing Airports Company South Africa (ACSA). Fifa spokesman Nicolas Maingot promised the football body would look at the cases of fans affected by flight problems.

There were other reports of emotions running high on the affected planes. Some passengers shouted and screamed at cabin crew staff on the Kulula airline, according to the Star newspaper. A 37-year-old man broke down in tears when looking at his children crying over missing the semifinal, the paper said. Kiran Singh, who was with his 11-year-old twins, 14-year-old son and two nephews aged 16 and 21, had bought match tickets for R1,750 (£152) each but arrived at King Shaka airport only five minutes before the end of the game.

"We were devastated," he told the Star. "We had waited a whole month for the semifinal. We missed everything ... We saw nothing. I cried when I looked at my crying children. If ACSA had a heart, they would give us tickets to the final. We don't want money, we just want to go and see the game."

ACSA said problems arose because some VIP planes, which were supposed to land at King Shaka airport and later park at an old airport some 40 miles away, would not move. "The congestion problem was caused by some private airplanes [which] refused to move ... after landing, therefore blocking landing space for other planes," airports chief Monhla Hlahla told 702 Radio. "Priority had to be given to VIPs who were caught up in the situation. We had too many flights wanting to land and at some point we had to instruct them to turn back." The company insisted passengers would not be reimbursed.

The disarray was a rare setback for a tournament that has defied sceptics with its smooth running and few hiccups. Organisers have, perhaps prematurely, already hailed it an unqualified triumph.

Rich Mkhondo, spokesman for the World Cup local organising committee, told Reuters there was nothing the organisers could do about the incident now. "Unfortunately, these kind of things happen," he said. "We will be meeting with ACSA later today to make sure this doesn't happen again during the final."

Paris Hilton, meanwhile, posted on Twitter after last night's game: "Back in Johannesberg [sic] already. Shortest flight ever. Only 15 minutes."