Zimbabwe has blocked flights by South Africa's government-owned airline amid tensions over allegations that Zimbabwe's first lady assaulted a young model in Johannesburg.

A South African Airways flight was not allowed to take off from Zimbabwe's Harare airport for a trip to Johannesburg on Saturday.

Another flight from Johannesburg to Harare was also cancelled.

Authorities in Zimbabwe said the planes were blocked for failing to comply with civil aviation rules.

The move follows the grounding of an Air Zimbabwe flight at Johannesburg's main international airport on Friday.

Both countries said they imposed restrictions because the planes did not have a "foreign operator's permit".

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A South African Airways spokesman said officials had asked to see certain documents that had not been requested in two decades.

Allegations against Grace Mugabe

The tit-for-tat between the two countries comes as Zimbabwe's first lady, Grace Mugabe, faces allegations of assaulting a young South African female model at a luxury hotel in Johannesburg.

Twenty-year-old Gabriella Engels has accused Grace Mugabe of barging into a hotel room where Engels was waiting to meet one of Mugabe's sons on Sunday and whipping her with an extension cord.

South African police issued a "red alert" on Friday at the country's borders to prevent Mugabe from fleeing undetected.

Her whereabouts were not known on Friday, but South African police minister Fikile Mbalula said she remained in the country.

The 52-year-old, who has not yet been charged, has asked for diplomatic immunity in the case.

Lawyers for Engels have threatened to go to court if immunity is granted.

It is not clear whether Mugabe entered South Africa on a personal or diplomatic passport.

South Africa's government said it had not yet decided whether to grant the request for diplomatic immunity.

'No one is above the law'

Political analyst Ayesha Kajee said the first lady's arrest could lead to a political falling out.

"Those countries that have traditionally been supportive of Zimbabwe would lambast South Africa for arresting Mrs Mugabe and prosecuting her," Kajee told Al Jazeera.

A statement by South African Airways on Saturday did not mention the allegations against Zimbabwe's first lady.

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The case has overshadowed a two-day regional summit in the South African capital of Pretoria, which is being attended by Zimbabwe's President Robert Mugabe.

Outside the summit, some protested against Mugabe on Saturday, saying she should be prosecuted.

"Arrest Grace, please. Grace is a disgrace," some chanted.

"No one is above the law," Milton Bangamuseve, an activist, told Al Jazeera.

"The law of the country must reign supreme. If she is guilty she must be sentenced like any other citizen."