An estimated 250 people made the journey from Wales to the holy city of Mecca, near where the incident happened on Thursday.
The Muslim Council of Wales (MCW) had difficultly contacting some groups from Cardiff, Newport and Swansea.
All have now confirmed they are safe.
MCW general secretary Saleem Kidwai said he had made contact with all group leaders from Wales, and all those on the pilgrimages have been accounted for.
The MCW's director of projects Mohammed Alamgir said he is now ensuring adequate support services are available to the returning parties through its network of chaplains and Imams.
"There was great concern for families and many members of the Welsh Muslim community waited anxiously for news of their loved ones and friends. Prayers were offered across Wales hoping for good news," he said on Sunday.
"We all now wait for the outcome of the investigation launched by the Saudi government and hope for further safeguards to ensure the safety of pilgrims."
Along with those killed, a further 863 people were injured in the incident at Mina, which happened as two million pilgrims were taking part in the Hajj's last major rite.
All groups from Wales making the Hajj pilgrimage in Saudi Arabia where a stampede killed at least 717 have been accounted for, a Muslim leader has said.