According to preliminary information, 21 miners have been found alive at the depth of 1000 meters in Karl Marx mine in Yenakiyevo.
According to an UNIAN correspondent, at present the first four survivors are being brought to the surface.
The relatives of the miners were allowed to approach the pit, where the rescued miners are expected to appear.
This fact has been confirmed to UNIAN by Marina Nikitina, head of the local branch of work safety body the Committee for the Protection of Labour.
As UNIAN reported earlier, according to AFP, on Sunday Andriy Bondarenko, the regional head of the emergency situations ministry, had said: "The fate of 37 people who were in the mine when the explosion took place... remains unknown."
"If people were injured outside the mine, it is hard to imagine that people survived inside," the leader of the independent miners` union, Mikhailo Volynets, told AFP in Yenakiyevo, 60 kilometres (40 miles) east of Donetsk.
Rescuers reached a depth of 625 metres (2,050 feet) but could not go any further, Turchinov, head of the government committee investigating the accident, told a news conference, adding that they could hear voices coming from a depth of 700 metres (2,300 feet).
The blast occurred at around 5:00 am (0200 GMT) Sunday 1,000 meters (3,300 feet) below the surface of the Karl Marx mine in Yenakiyevo, north-east of the regional capital Donetsk, Bondarenko said.
The blast severely damaged the entrances to the mine which was opened in 1958.
Three women operating the elevator shaft were hospitalised with serious burns and at least one other person on the surface was injured, said Marina Nikitina, head of the local branch of work safety body the Committee for the Protection of Labour.
The mine, opened in 1958 and one of the oldest in Ukraine, was closed down on Saturday due to safety violations and only a skeleton staff was working at the time of the blast, according to the emergency ministry.
But some miners told Kanal 5 television that work at the mine had continued as usual into Sunday morning in spite of the supposed closure.
"If the mine was up and running and coal was being produced in spite of the closure the public prosecutor will get involved and punishment will no doubt be severe," said Turchinov.
Police closed off the mine and journalists were only allowed to enter the administrative building, an AFP photographer said.
Work has been suspended at 20 mines in the region following an explosion on May 23 that killed 11 people, one of a series of disasters to strike the region`s aging pits in recent years.
In November last year, a gas explosion at the Zasiadko mine in Donetsk killed 101 miners. The accident was the worst of its kind in this former Soviet republic.
