The loud explosions and wailing sirens in rebel-held territory in eastern Ukraine were getting more frequent, so when the evacuation order came, Elena Sokela decided it was time to get her son to safety.

"We didn't want to wait until it was too late. Better to get out now," the 40-year-old told AFP Saturday at a border crossing between the rebel Donetsk region and Russia, a day after the order to evacuate came down.

There was a steady flow of people acting on the order to leave, crossing between wire fencing topped with Russian flags on a bright morning at the Avila Uspenka checkpoint into Russia.

On Friday evening, leaders of two separatist republics in east Ukraine ordered women and children to flee and as soon as possible make their way to Russia.

Their poor and industrial rebel-controlled territories in Ukraine have been at the centre of weeks of tensions between Russia and the West.

Conflict monitors have warned of a sharp escalation in ceasefire violations in fighting between Ukraine's army and the separatists, a trend Sokela herself could attest to.

In her hometown of Shakhtarsk, she said, "we can hear everything perfectly clearly. There were explosions on Thursday. Some heavy stuff was coming down."

The US government earlier hit out at the orders, saying the move by Moscow-backed rebels was a "cynical" effort by Moscow to deflect from what the West fears is an imminent Russian invasion.

At the checkpoint Saturday there was a steady stream of elderly women and children, dressed in puffy coats on a crisp winter day and dragging wheelie bags.

Sokela was bringing her 16-year-old son to stay with his grandmother in Russia "where it's calm" but planned to return herself.

"Let's stay for a week and come back. Or maybe the school will be closed. No one has said anything yet," Sokela said.

Separatist leaders have announced plans to get hundreds of thousands of people out of the territory and into Russia, but AFP journalists at the crossing Saturday witnessed no mass exodus.

Several Russian regions have announced they will house Donetsk and Lugansk residents who have been ordered to leave
Several Russian regions have announced they will house Donetsk and Lugansk residents who have been ordered to leave AFP / Andrey BORODULIN

Ten school buses waiting to ferry arrivals stood empty and 15 tents set up by the emergencies ministry on the Russian side of the crossing had no one to house.

So far, separatist officials have said fewer than 20,000 people have left, a fraction of the region's estimated population of three million people.

Still, Russian authorities were readying for a large influx, with officials in the Rostov region bordering Ukraine declaring a state of emergency and saying places were being prepared for nearly 900,000 people.

The head of Russia's emergencies ministry, who was dispatched by the Kremlin to Rostov, said Saturday some 400 people and 150 vehicles were in place to receive people arriving from separatist territory.

Several other nearby regions have announced they will house Donetsk and Lugansk residents.

President Vladimir Putin on Friday ordered handouts of 10,000 rubles (about 100 euros) to evacuees and health officials have said those entering Russia can be tested for the coronavirus and vaccinated.

Many, however, hope the displacement will be temporary.

The head of the so-called Donetsk People's Republic Denis Pushilin met with residents leaving, Russian news agencies reported, to offer reassurances.

"I hope it won't be for long," he was cited as saying. "But safety is paramount."

"I'll be here in Russia today to do my errands and then I'll come back later," she said.

"I'm a medical professional. I can't abandon people. I didn't leave them in 2014, I won't leave them now," she added.