Three bridges have been destroyed on roads leading into the city of Donetsk on Monday ahead of an expected offensive from government forces.
It was unclear who was behind the explosions but Ukrainian media said the bridges were blown up by rebels as Ukraine's military advanced.
Ukrainian troops regained control of the key rebel strongholds of Sloviansk and Kramatorsk on Saturday.
A journalist in Donetsk says civilians in the city are preparing for fighting.
"For the moment there are no gunfights but people are really scared," Yevgeny Shibalov told BBC Newshour.
"A lot of shops are closed and some banks officially declared they are closing their branches in the city," he added.
Separatist fighters driven out of Sloviansk and Kramatorsk at the weekend have regrouped in Donetsk.
A railway line in the village of Novobakhmutivka that crosses over a main road out of Donetsk was targeted, leaving a large cargo train dangling across the void.
A witness told the AP news agency that he saw a group of camouflaged men get into their cars and head towards Donetsk shortly before the bridge collapsed after an explosion.
Two other bridges on roads leading from Sloviansk to Donetsk were also destroyed in the villages of Zakitne and Seleznevka, Ukraine's transportation authority said on Monday.
Ukraine's 5 Channel TV said militants had carried out the attacks, quoting state railways as saying repairing the bridges could take a month and a half.
Mykhaylo Koval, a senior Ukrainian security official, said government troops were preparing to continue the operation against the separatists.
"There is a clear strategic plan, which has been approved. The plan is focused on two major regional centres: Luhansk and Donetsk. These cities will be completely blockaded," Mr Koval said.
"These measures will result in the separatists - let us call them bandits - being forced to lay down arms."
Meanwhile, Ukraine's richest man, coal and steel magnate Rinat Akhmetov, pleaded with the government on Monday not to bomb his home city of Donetsk and the wider Donbass region.
Mr Akhmetov, whose fortune is estimated at more than $11bn (£6.5bn), said government forces should show restraint in their operations in the east of Ukraine.
"Donetsk must not be bombed. Donbass must not be bombed. Cities, towns and infrastructure must not be destroyed," he told Ukrainian TV. "We must avoid suffering and deaths of peaceful people."
The level of support for the militants in the two regional capitals is unclear. However, several thousand people joined a rally in Donetsk on Sunday attended by leaders of the self-declared Donetsk People's Republic.
The separatists declared independence in both Donetsk and Luhansk regions after Russia annexed the Crimea region in March.
On Sunday, the website of Ukrainian President Petro Poroshenko said the national flag had been raised in the towns of Artemivsk and Druzhkivka.
The two towns are not considered as strategic as Sloviansk, but retaking them indicates momentum is currently with government forces, says the BBC's David Stern in Kiev says.
In a separate development, the government in Kiev said it had begun transferring pensions to Sloviansk and the nearby city of Kramatorsk, which was also recaptured from rebels on Saturday.
Donetsk regional governor Serhiy Taruta said he thought electricity and health services could be up and running again during the week.
"The task now is to get the hospital working since it is without electricity; then water, sewage, and we will work on all social services," he was quoted as saying by Interfax Ukraine news agency.
Representatives from Ukraine, Russia and the Organization for Security and Co-operation (OSCE) in Europe met on Sunday to discuss the situation in eastern Ukraine, but OSCE officials said no breakthrough was achieved.
Tensions remain high, our correspondent adds; in Kiev, local reports said unknown gunmen had opened fire early on Monday morning at a tent camp in the city centre, causing injuries, but no deaths.
Russian press reaction to the re-taking of Sloviansk
Moskovsky Komsomolets: "For many Russians, the incorporation of Crimea was the happiest political moment in many years. Russia showed what it can do if it really wants to. The bloody slaughter in south-eastern Ukraine has shown the opposite. Russia has become aware of its limitations. We are powerless to avert the tragedy taking place just across our border."
Rossiyskaya Gazeta: "Despite bravura reports, this 'victory' has been a Pyrrhic one for the Ukrainian army. In the wake of the massive ground and air bombardment, Sloviansk, Kramatorsk and especially adjacent towns are more than half destroyed - they have been turned into ghost towns. The destroyed infrastructure will take weeks, if not months, to rebuild."
Kommersant: "A breakthrough is emerging in the confrontation in eastern Ukraine. The capture of Sloviansk, which was considered to be the symbol of resistance, has been the government forces' biggest success over two months of fighting. Though the militia has called its retreat a 'tactical manoeuvre' and Kiev has a big temptation to fight until a total victory, the two sides will have to reach an agreement, otherwise this will be a long war."
Vedomosti: "The [pro-Russian militants'] departure can mean the start of an urban guerrilla war, similar to the kind practised by leftists and some nationalists in Latin America and Europe in between the 1950s and 1980s. They tried to undermine the state by resorting to quick attacks and assaults on government institutions, police and army units, raiding banks and factories, and also taking hostages."
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