The seizure of Krasnogorovka and Staromikhailovka, towns just outside Donetsk, brought the army to the edge of one of the last cities still in rebel hands following its advances in the past month. The other is Luhansk, near the border with Russia.
Shelling near the area where a Malaysian airliner was downed last month forced international experts to stop their search for victims at one part of the crash site, but a local ceasefire enabled them to work unhindered at the main part.
Working with sniffer dogs, they recovered more human remains and personal belongings for examination, officials said.
Diplomatic efforts to end the wider conflict, the worst standoff between Moscow and the West since the Cold War ended in 1991, show no sign of progress.
British Prime Minister David Cameron said NATO must rethink its ties with Moscow and called for it to overhaul itself to be better able to defend member states from a potential Russian military threat.
"Six months into the Russia-Ukraine crisis we must agree on long-term measures to strengthen our ability to respond quickly to any threat, to reassure those allies who fear for their own country's security and to deter any Russian aggression," he wrote in a letter to fellow alliance leaders and NATO Secretary General Anders Fogh Rasmussen.
U.S. President Barack Obama also vented his frustration with Russia after speaking to President Vladimir Putin by telephone on Friday. Obama told reporters the United States had done "everything that we can do," short of going to war, to persuade Putin of the need to resolve the crisis diplomatically.
"But sometimes people don't always act rationally, and they don't always act based on their medium- or long-term interests," he said.
RUSSIA SEES EU "DOUBLE STANDARDS"
The United States and the European Union imposed new sanctions on Moscow this week after accusing Putin of failing to use his influence with the separatists to end the fighting in the mainly Russian-speaking east.
Putin denies arming the rebels and accuses the West of pursuing a policy of containment against Moscow, using a Cold War-era phrase to suggest Washington wants to reduce Russia's global influence.
In a new attack on Western policy, Russia's Foreign Ministry accused the EU of "double standards", saying it was punishing the Russian defense sector with the latest sanctions but "on the quiet" had ended restrictions on sales of military technology and equipment to Ukraine.
"We call again on our EU colleagues to follow sound logic and not conjecture and goading from Washington," the Foreign Ministry said, questioning the EU's "dubious political goals."
The EU overcame the reservations of some business leaders, particularly in Germany, to agree the latest sanctions. Indicating this would have an impact on the EU's largest economy, the head of Germany's Ifo institute said economic growth would shrink towards zero in the second quarter because of the Ukraine crisis and the new sanctions.
The rebellion in east Ukraine began in mid-April, two months after Ukrainian President Viktor Yanukovich was ousted after he shifted policy away from the EU towards Moscow, and one month after Russia annexed the Crimea peninsula from Ukraine.
The army has been making advances against the separatists since President Petro Poroshenko stepped up the military campaign against them after his election in May, and fighting intensified after the Malaysian airliner was downed on July 17.
The United States says the separatists probably shot down the plane by mistake with a Russian-supplied missile. The rebels and Moscow deny the accusation and blame the disaster, in which 298 people were killed, on Kiev.
The Ukrainian military reported three cases of shooting from across the border with Russia overnight, a charge it has leveled at Moscow increasingly often.
Moscow denies such accusations, and Russia's RIA news agency quoted border guards as saying nine shells had been fired from Ukrainian territory onto Russian soil.
(Additional reporting by Pavel Polityuk and Aleksandar Vasovic in Kiev, Alexander Winning in Moscow and Philip Blenkinsop in Brussels; Writing by Timothy Heritage; Editing by Janet Lawrence and Robin Pomeroy)