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The Saudi-led coalition fighting rebels in Yemen admitted on Saturday that "mistakes" had been made in an August airstrike that killed 51 people, including 40 children.

The bombing on a crowded market in part of northern Yemen held by Houthi rebels killed a total of 51 people, according to the Red Cross.

Fifty-six children were also among the 79 people wounded in the August 9 strike on Saada province, a stronghold of the Iran-backed Houthis bordering Saudi Arabia.

The incident sparked a wave of international anger and calls by the United Nations Security Council for a "credible and transparent" investigation.

Coalition spokesman Mansour al-Mansour said a coalition probe had found that errors were made prior to the strike, and called for those responsible to be "punished".

He told a press conference in Riyadh that "an order had been given not to target the bus, which was among civilians, but the order arrived late".

Another error was that "the target did not pose an immediate threat and that targeting the bus in a residential area was unjustified at that time," he said. 

The coalition had claimed to have targeted a bus carrying rebels.

Mansour repeated Saturday that the bus had been "transporting Houthi leaders" according to information from intelligence services.

But Mansour admitted the strike had "caused collateral damage".

The coalition has been accused of committing numerous human rights violations in Yemen. A report from the UN last week said many of the violations could amount to "war crimes".

It has recognised some of the incidents, but the coalition regularly accuses Houthis of hiding among civilians or using them as human shields. 

The Saudi-led coalition intervened in Yemen in March 2015 after the Houthis ousted President Abedrabbo Mansour Hadi's government from the capital Sanaa and seized swathes of the country.