About 250 people are believed to have made the journey from Wales to the holy city of Mecca, Saudi Arabia, near where the incident happened on Thursday.
Saleem Kidwai, of the Muslim Council of Wales (MCW), said members had difficultly contacting groups in Mecca.
He added there is no alarm that a group from Cardiff has not been in touch.
Elsewhere, Muslim leaders in Newport and Swansea say they are not aware of any missing people from their cities.
Mr Kidwai said: "We have spoken to the families of the groups that haven't been in contact with them. They don't want to say anything until the situation becomes clear. They just hope and pray everything is okay.
"It is a horrific event, with no news coming out. We hope that there will be good news but we will be providing counselling facilities if necessary.
"We are constantly trying to ring and get some information. Even our contacts in that part of the world are trying to get some information. Other organisations are very active in trying to find information.
"We hope that the situation will improve. The families find solace and tranquillity in faith. It was not a holy day, but they can have solace in their religion. We're praying for those unaccounted for."
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.
One Welsh group taking part in the Hajj pilgrimage when a stampede killed at least 717 people is yet to make contact, a Muslim leader has said.