Rescuers who were set to travel to Turkey and Syria felt “sick” after being told to leave.
Dog handlers Emma Whittle and Brian Jones had hoped to travel with a team of detector dogs to help after the earthquake.
The death toll currently stands at more than 7,200.
Ms. Whittle and Mr. Jones hoped they could help rescue survivors from the rubble with their specialized search dogs.
Jones, from British International Rescue and Search Dogs (BIRSD), based in Penmaenmawr, County Conwy, said he was feeling “very sick because everything helps”.
He said the dogs could help identify areas where people could become trapped.
“Instead of 30 square yards, it can be five square yards and we know there’s a smell coming from the rubble in that area,” he explained.
“So we know we can mark that area so Serve On will come and remove the body.”
Serve On is a humanitarian crisis organization working at home and abroad.
Jones said the UK government had sent a team on Monday.
He said: “I think they had four dogs with them. We asked if they needed our services, they said ‘yes, thanks for offering’.
“Then Serve On put us on hold. Overnight we sat there.
“In the morning we received a notification from Serve On that they had been removed and could not enter the country.
“The problem is between our government and the Syrian government. They couldn’t get permission to leave.”
Ms Whittle hasn’t worked before after an earthquake, but was called to help after a landslide in Malaysia.
“Time is of the essence, the sooner we get out the better,” he said.
The disaster struck when a 7.8 magnitude earthquake struck near the city of Gaziantep, Turkey, early Monday morning.
This was followed by a magnitude 7.5 tremor that had its epicenter in Elbistan, in the south of the country.
Firefighters from across the UK, including the West and Central Wales and South Wales fire and rescue services, are heading to Turkey to help with the rescue efforts.
The Welsh Institute of International Affairs and the Welsh Syrian Society are asking people to donate to organizations on the ground.
Mohammed Alhadj Ali of the Syrian Welsh Society called the situation “catastrophic”.
He said: “They need medical help, they need shelter, help and support to get people out of rooms.
“That’s the top priority to be honest with you.”
Dr. Ali said that his friends had told him that the winter in Syria had been difficult.
There was no fuel for heating, he said, food was scarce and prices were rising.
“They had air raids, shelling, flooding, harsh winters and difficult summers,” he said.
“It has been a decade of tragedy in Syria.”
Welsh Social Justice Minister Jane Hutt said she had seen a sympathetic message to the Turkish ambassador.