Rescuers poised to travel to Turkey and Syria have felt “sick” after being told to step down.
Dog handlers Emma Whittle and Brian Jones were expected to travel with a team of detection dogs to help after the earthquake.
The death toll currently stands at over 7,200.
Mrs Whittle and Mr Jones had hoped they could help rescue survivors from the wreckage with their specialized search dogs.
Mr Jones, of British International Rescue and Search Dogs (BIRSD), which is based in Penmaenmawr, County Conwy, said he felt “very bad because every little bit helps”.
He said the dogs could help pinpoint areas where people might be trapped.
“Instead of 30 square meters, it could be five square meters and we know there is a smell coming out of the rubble in that area,” he explained.
“So we know we can mark that area for Serve On to come and extract the body.”
Serve On is a crisis relief organization working at home and abroad.
Mr Jones said a team was dispatched by the British government on Monday.
She said: “I think they had four dogs with them. We asked if they needed our services, they said ‘yes, thanks for the offer’.
“We were then put on standby by Serve On. Overnight we just sat there.
“In the morning we received a notification from Serve On that they had resigned and could not enter the country.
“The problem is between our government and the Syrian government. They couldn’t get permission to leave.”
Mrs Whittle has never worked following an earthquake, but was called in to help after a landslide in Malaysia.
“Time is of the essence, the sooner we get out the better,” she said.
The disaster struck when a magnitude 7.8 earthquake struck early Monday morning near the city of Gaziantep, Turkey.
This was followed by a 7.5 magnitude quake which had its epicenter in Elbistan, in the south of the country.
On Monday, 76 rescue specialists were sent by the British government to help search for survivors.
The Welsh Institute for International Affairs and the Syrian Welsh Society are asking people to donate to organizations on the ground.
Mohammed Alhadj Ali, of the Syrian Welsh Society, said the situation was “catastrophic”.
He said: ‘They need medical care, they need shelters, help and support to get people out of rooms.
“This is the top priority to be honest with you.”
Dr Ali said friends had told him the winter in Syria had been difficult.
There was no fuel for heating, he said, food was scarce and prices were rising.
“They’ve had airstrikes, they’ve had the bombings, the floods, hard winters and tough summers,” he said.
“It was a decade of tragedy in Syria.”
Welsh social justice minister Jane Hutt said she had seen a message of sympathy with the Turkish ambassador.