Ukrainian forces have been pushing rebel units back towards their two main urban strongholds of Donetsk and Luhansk and have sought to encircle them in several places, including in the wider area where a Malaysian airliner crashed on July 17.
Officials said 14 people, including five children, were killed in fighting on Monday evening in the town of Gorlovka/Horlivka, one of several spots that saw fierce battles between the rival forces in the last few days.
In the city of Luhansk, officials said five civilians were killed when shelling hit a retirement home.
"The enemy is throwing everything it has into the battle to complete encirclement of the DNR," rebel commander Igor Strelkov told journalists in Donetsk on Monday evening, referring to the self-proclaimed "Donetsk People's Republic".
"We were astonished by how much amour they threw into this battle," said Strelkov, a Russian national, sporting a camouflage T-shirt and trousers.
A rebel source in Donetsk said reinforcements including military equipment and fighters had crossed the nearby border with Russia into Ukraine. Reuters was not able to confirm that independently.
Rebel leaders insist publicly that Moscow is not supplying them. Russia also denies Western accusations that it is supporting the rebellion with arms and troops.
Leaders of the United States and major European powers agreed in a teleconference on Monday to impose wider sanctions on Russia's banking, technology and arms sectors over its alleged backing for the separatists.
The rebels say 7,400 Ukrainian soldiers have been killed or injured since Kiev launched what it calls its "anti-terrorist" operation against separatists in the east in early May. Kiev puts the toll at fewer than 1,500.
A humanitarian corridor was due to open in Luhansk for six hours on Tuesday to allow residents to flee the fighting, but officials said they could not guarantee full safety.
The United Nations says more than 100,000 people have already fled Ukraine's tumultuous east.
A team of international experts including 38 Dutch and 12 Australian police will try to get to the plane crash site for a third day on Tuesday after fighting in the rebel-held area forced them to turn back on Sunday and Monday.
Fighting has impeded recovery of some of the remains from flight MH17 and undermined a probe that will be crucial as Kiev and the West trade recriminations with Moscow over the downing of the Boeing airliner. All 298 people on board were killed.
The international experts said if and when they get to the crash site, spread over a large area of fields, their first priority would be to recover any remaining body parts and then remove personal belongings from the area.
The Organisation of Security and Cooperation in Europe, the first international body to get several experts to the site after the plane went down, was negotiating an access corridor overnight with both rebels and Ukrainian troops.