The coalition itself, following calls from the UN and United States, announced an investigation into Thursday's strike.

In New York, Britain's Ambassador Karen Pierce, whose country holds the Security Council presidency, told reporters after a closed-door meeting on Yemen that "if any investigation that is held is not credible, the council will obviously want to review that".

The raid that hit the bus in Dahyan market in the Huthi rebel stronghold of Saada also injured at least 48 others, including 30 children, according to the International Committee for the Red Cross.

An AFP photographer at the scene said the bus transporting the children had been turned into a mass of twisted metal, and that the remains of victims and personal items were still scattered across the ground on Friday.

"There are remains everywhere, we are still trying to confirm identies," Yahya Shayem, a health official in Saada, told AFP.

The coalition, which has been fighting Yemen's rebels since 2015, claimed the bus was carrying "Huthi combatants".

It initially said the coalition had carried out a "legitimate military action", targeting a bus in response to a deadly missile attack on Saudi Arabia on Wednesday by Huthi rebels.

At a press conference in Dahyan on Friday, Huthi health minister Taha al-Mutawakel put the death toll from the "horrible crime" at 51 people, including 40 children.

"This toll is not final... a lot of people are missing and the remains are still scattered around the crime scene and nearby," he said.

The Red Cross could not immediately confirm the new figures.

- Children 'excited' for trip -

At the time of the attack, the children were on a bus heading back to school "from a picnic", the Save the Children charity said, quoting its staff.

One of the children's teachers told AFP the pupils had eagerly awaited the journey.

"The mothers told me that their children did not sleep for two days because they are were too excited to take part in this trip," said Yahya Hussein.

The Huthis' Islamic affairs ministry said the children were from a Koranic school.

In the wake of international criticism, the coalition said it would open an investigation.

The decision followed reports about "a passenger bus which suffered collateral damage in this operation", a senior coalition official said, quoted by the state-run Saudi Press Agency.

The Security Council met behind closed doors on Friday to discuss the attack, at the request of five countries which are non-permanent council members.

"We have seen the images of children who died," Dutch Deputy Ambassador Lise Gregoire-van Haaren told reporters. "What is essential at this moment in time is to have a credible and independent investigation."

UN humanitarian coordinator in Yemen, Lise Grande, deplored the death of the children as "heart-breaking".

"The costs of this terrible war rise higher and higher," Grande said of the Yemen conflict.

- Rebel missile attacks -

The coalition, which also includes the United Arab Emirates, intervened in 2015 in Yemen to try to restore the government after the rebels drove it out of the capital Sanaa.

Coalition spokesman Turki al-Maliki on Thursday said claims by aid organisations that children were inside the bus were "misleading", and that "the elements inside the bus were Huthi combatants".

Saudi Arabia shot down a missile fired by the Huthis on Wednesday, with debris killing a Yemeni man and wounding 11 others, the coalition said.

The missile was fired from the rebel-held Yemeni province of Amran towards the Saudi city of Jizan, the coalition said.

On Friday, the coalition said it intercepted and destroyed two more ballistic missiles fired by the Huthis from Saada towards Jizan. No damage or injuries were reported.

The war in impoverished Yemen has left nearly 10,000 people dead and unleashed what the UN describes as the world's worst humanitarian crisis.

UN envoy to Yemen, Martin Griffiths told the Security Council last week "a political solution" to Yemen's war was "available" and that the warring sides would be invited to talks on September 6 in Geneva.

UN-brokered negotiations on Yemen broke down in 2016 amid demands for a rebel withdrawal from key cities and power-sharing with the Saudi-backed government.