ANTAKYA, Feb 7 (Reuters) - The death toll of a devastating earthquake in southern Turkey and Syria jumped to more than 7,800 people on Tuesday as rescuers worked against time in harsh winter conditions to dig survivors out of the rubble of collapsed buildings.

As the scale of the disaster became ever more apparent, the death toll looked likely to rise considerably. One U.N. official said thousands of children may have died.

Turkish President Tayyip Erdogan declared a state of emergency in 10 provinces. But residents in several damaged Turkish cities voiced anger and despair at what they said was a slow and inadequate response from the authorities to the deadliest earthquake to hit Turkey since 1999.

"There is not even a single person here. We are under the snow, without a home, without anything," said Murat Alinak, whose home in Malatya had collapsed and whose relatives are missing. "What shall I do, where can I go?"

Monday's magnitude 7.8 quake, followed hours later by a second one almost as powerful, toppled thousands of buildings including hospitals, schools and apartment blocks, injured tens of thousands, and left countless people homeless in Turkey and northern Syria.

Rescue workers struggled to reach some of the worst-hit areas, held back by destroyed roads, poor weather and a lack of resources and heavy equipment. Some areas were without fuel and electricity.

With little immediate help at hand, residents picked through rubble sometimes without even basic tools in a desperate hunt for survivors.

Aid officials voiced particular concern about the situation in Syria, already afflicted by a humanitarian crisis after nearly 12 years of civil war.

Erdogan declared 10 Turkish provinces a disaster zone and imposed a state of emergency for three months that will permit the government to bypass parliament in enacting new laws and to limit or suspend rights and freedoms.

The government will open up hotels in the tourism hub of Antalya to temporarily house people impacted by the quakes, said Erdogan, who faces a national election in three months' time.

The death toll in Turkey rose to 5,894, Vice President Fuat Oktay said. More than 34,000 were injured. In Syria, the toll was at least 1,932, according to the government and a rescue service in the insurgent-held northwest.