Pro-Russian separatists in eastern Ukraine have suffered dramatic setbacks after top military chiefs quit and Kiev's forces pummelled their strongholds, cutting off a key rebel-held city from the Russian border.

Kiev's advance came as the Russian "humanitarian" convoy parked up close to the frontier, with doubts still swirling over what the trucks contained and whether they would be allowed to cross.

According to reports in two British newspapers, a smaller group of Russian vehicles, including armoured cars, did cross the border into Ukraine late Thursday.

The Daily Telegraph "witnessed a column of vehicles including both armoured personal carriers and soft-skinned lorries crossing into Ukraine at an obscure border crossing near the Russian town of Donetsk."

The Guardian daily said a column of 23 armoured personnel carriers and other vehicles crossed near Donetsk, about 200 kilometres from the Ukrainian town of the same name.

The separatist leadership has showed signs of unravelling following four months of fighting that have left more than 2,000 dead and many residents in the region without power or running water, and with dwindling food supplies.

The rebels said their main military chief, Igor Strelkov, had resigned while the rebel commander in the second-biggest insurgent stronghold of Lugansk, Valery Bolotov, told Russian television he was "temporarily" stepping down because of earlier injuries.

The announcements came after Ukraine's military said it had completely surrounded Lugansk, cutting all links to the border with Russia, which Kiev believes has been supplying the insurgents with weapons.

Intense shelling on Lugansk and the main insurgent bastion of Donetsk in eastern Ukraine left more than 25 people dead, while Ukrainian forces reported nine troops dead and 18 injured over the past day.

While reiterating its support for Kiev, Washington urged its ally to exercise restraint and keep civilian casualties to a minimum.

- US urges restraint -

"We've stressed the importance of showing restraint to minimise casualties among the civilian... population," State Department spokeswoman Marie Harf told reporters.

"We call on the Ukrainians to take every step to avoid the local population as they try to free the city from the separatists," Harf said.

The Russian foreign ministry on Thursday called for all sides to accept an "urgent" ceasefire, saying the situation in the east was "extremely serious".

Russia's convoy of nearly 300 white-tarpaulin-covered lorries meanwhile halted Thursday near the town of Kamensk-Shakhtinsky, some 50 kilometres (30 miles) from eastern Ukraine, Russian media reported.

A local source told AFP the lorries could try to cross the border near the Ukrainian town of Izvaryne, but it was unclear when this might happen or whether Kiev would allow them to pass.

Russian media said the convoy, which left the Moscow region on Tuesday, carried more than 1,800 tonnes of supplies including medical equipment, baby food, sleeping bags and electric generators.

Ukraine has repeatedly said it will not allow Russian lorries onto its territory and that any aid would have to be unloaded at the border under the supervision of the International Committee of the Red Cross (ICRC).

President Petro Poroshenko's office on Wednesday suggested the aid could be allowed in, but only if it was inspected by Ukrainian border guards and international monitors.

Fears have mounted that the aid mission could escalate a conflict that has already brought tensions between Russia and the West to a post-Cold War high.

Ukraine and the West have warned that Moscow's convoy could be a "Trojan horse" bringing military help to pro-Russian insurgents, who have been losing ground to government troops in the east.

Ukraine dispatched its own aid convoys to the industrial east as it tried to race Moscow to hand out much-needed assistance to people in the blighted region.

Kiev said it was sending 75 lorries with 800 tonnes of aid to the Lugansk region.

- Heavy shelling in Donetsk -

The need for aid was clear, as heavy shelling smashed into the centre of Donetsk, once a bustling city of one million.

Health authorities said 74 civilians were killed and 116 wounded over the past three days.

More than 2,000 people have died in the four-month conflict, the UN human rights agency said Wednesday, noting the death toll had doubled in just two weeks.

Some 285,000 people are also estimated to have fled their homes in the east.

The crisis has led to tit-for-tat sanctions between the West and Russia over Moscow's alleged support for the insurgency in eastern Ukraine.

On Thursday President Vladimir Putin said Russia should not let the West treat it "with disdain" but also should not "fence itself off from the outside world".

Putin will meet his Finnish counterpart Sauli Niinisto for talks in the southern Russia town of Sochi on Friday.

Finland has been one of the EU countries most hurt by the rising tensions and tit-for-tat sanctions between Moscow and the West over the crisis in Ukraine.