The Saudi-led coalition announced earlier that it had ordered an investigation into the air strike on Thursday that also wounded at least 48 other people in the rebel stronghold of Saada, in the north of the country.
British ambassador Karen Pierce, who holds the presidency of the council, told reporters after a closed-door meeting in Yemen that "if any investigation is carried out is not credible, the council will obviously want to review that" and decide " if more is needed. "
The council did not order a separate investigation, but "now will consult with the UN and others on how the investigation can be carried out," Pierce said.
The council met at the request of five countries: Bolivia, the Netherlands, Peru, Poland and Sweden, which are all non-permanent council members.
Kuwait, also a non-permanent council member, is part of the Saudi-led coalition fighting the Huthi rebels in Yemen.
The United States, France and Britain, three of the five permanent members of the council, have supported the Saudi coalition in their military campaign, but have expressed concern about the large number of civilian casualties.
Prior to the meeting, the Netherlands had stressed that the investigation should be independent, suggesting that the coalition's decision to open an investigation was insufficient.
"We have seen images of children who died," Dutch deputy mayor Lise Gregoire-van Haaren told reporters.
"What is essential at this moment in time is to have a credible and independent investigation."
The council did not specify in the statement agreed to the press that the investigation should be independent, a demand that the secretary general of the UN, Antonio Guterres, also made in a statement condemning the attack on Thursday.
The members of the Council expressed their "great concern" and "asked for a credible and transparent investigation," Pierce said.
Human Rights Watch criticized the council's inability to demand an impartial investigation.
"The sad truth is that the Saudis have been given the opportunity to investigate themselves and the results are laughable," said HRW UN Deputy Director, Akshaya Kumar.
Of the 75 cases of civilian deaths investigated by the coalition, only two resulted in an admission of guilt, he said.
Last year, the coalition was placed on a UN blacklist of child rights violators for killing or wounding 683 children and attacking dozens of schools and hospitals.
Since 2015, Saudi Arabia has been leading a military campaign to restore the internationally recognized government to power and push back the Huthis, who still have the capital, Sanaa.
The war left almost 10,000 dead and unleashed what the United Nations describes as the worst humanitarian crisis in the world.