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.

Dozens more were injured in the accident near the town of Bambari, about 300km (186 miles) north-east of the capital Bangui.
Most of the victims are said to be traders heading to a nearby market.
Local residents often travel in overloaded lorries due to lack of other transportation in the country.
The cause of Wednesday's crash is now being investigated.
A local lawmaker said the lorry was travelling faster than normal.
"They were driving fast to make it to the market on time. That's what probably caused the accident," Amaseka Topi told Reuters news agency.
Dozens of injured people are being treated in Bambari's hospital. There are fears that the death toll could rise further.
Years of neglect have left much of the Central African Republic's road system in ruins, and safety regulations are rarely enforced.
The poor landlocked country has been wracked by conflict along religious and ethnic lines since 2013.

Heidi Gannon was born in Wales and her sister Jo Baines was born in England about two hours afterwards.
Their mum didn't know she was having twins.
A set of twins were born in England and Scotland in 2012 and were thought to be the first to be born in different countries but Heidi and Jo were born much earlier, in 1976.
The family has been in touch with Guinness World Records which has confirmed they will update their records.
A spokesperson said: "We were made aware of Ms Baines and Ms Gannon's claim for this record last week and after some research involving our twins consultant we have been able to verify that they are indeed the first twins born in different countries."

The ex-Middlesex captain moved to Lord's from Essex in 2009 and has scored 5,977 first-class runs since making his debut for Kent in 2005.
Dexter, 31, has taken 28 wickets in all formats this season and is two scalps short of his 100th first-class wicket.
"It's a bit of a coup for the club," elite performance director Andrew McDonald told BBC Radio Leicester.
"It is nice to have someone of Dexter's experience, leadership qualities and skill set join the club.
"What he will offer in all three formats of the game is going to be superb. We felt that the little bit of extra experience was needed for this group to be the real deal next season.
"It is a good sign when players like Dexter approach us. It shows the steps forward we are taking on and off the field."
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.
[NEXT_CONCEPT]
At least 77 people have been killed after a lorry loaded with passengers and goods crashed in the Central African Republic, officials say.
[NEXT_CONCEPT]
Twins claim world record title as the first pair to be born in different countries - nearly 40 years later.
[NEXT_CONCEPT]
Leicestershire have signed Middlesex all-rounder Neil Dexter on a three-year contract from the start of next season.