Reuters reporters heard sounds of distant gunfire coming from the south of the city and local media reported brief outbreaks of fighting on the outskirts, although this could not be independently confirmed.
However, this appeared minor compared with on Monday and Tuesday when government forces killed dozens of rebel fighters in an assault to retake Donetsk International Airport, which the rebels had seized the morning after Ukrainians overwhelmingly elected Petro Poroshenko as president.
Pro-Moscow gunmen have declared the city of a million people capital of an independent Donetsk People's Republic. On Wednesday their leader Denis Pushilin appealed again for Russia's help. "The residents of the Donetsk People's Republic are on the verge of a humanitarian catastrophe," he said. "We are Russians and this is precisely why they are killing us. We want to become part of Russia."
In Moscow, Russian Foreign Minister Sergei Lavrov accused the West of pushing Ukraine into "the abyss of fratricidal war", and reiterated his call for an end to Kiev's military offensive. His ministry urged Kiev to let it send humanitarian aid to civilians trapped by the fighting in eastern Ukraine.
The rebels' plight puts pressure on President Vladimir Putin to act, even though he has reduced the number of forces he has massed on Ukraine's eastern border and has said he would recognise the outcome of Sunday's election in Ukraine.
Rebel fighters were strengthening their barricades with sandbags on the road to the airport near the hulk of a truck where many of them were killed by government fire on Monday.
The assault was the first time Kiev has unleashed its full military force against the fighters after weeks of restraint. Morgues were filled on Tuesday with bodies of rebel gunmen, some missing limbs.
The separatist authorities say as many as 50 died, including a truckload of wounded fighters blasted apart as they were driven away from the battlefield. The government said it suffered no losses in the operation, when its aircraft strafed the airport and paratroops landed to reclaim it.
A STATE OF WAR
Poroshenko, 48, a billionaire confectionary magnate who became the first Ukrainian since 1991 to win the presidency outright in a single round of voting, repeated his promise to restore government control rapidly over secessionist-held areas.
"We are in a state of war in the east. Crimea is occupied by Russia and there is great instability. We must react," he told Germany's Bild newspaper.
"We will no longer permit these terrorists to kidnap and shoot people, occupy buildings or suspend the law. We will put an end to these horrors - a real war is being waged against our country," said Poroshenko, who is expected to be inaugurated within two weeks.
His swift offensive has thrown down a challenge to Putin, who made defending Russians in other parts of the former Soviet Union a pillar of his rule since declaring his right to use military force in Ukraine in March.
"I have no doubt that Putin could end the fighting using his direct influence," Poroshenko said. "I definitely want to speak with Putin and hold talks to stabilise the situation."
Moscow says it is willing to work with Poroshenko but has no plans for him to visit. However, Poroshenko will attend commemorations of the 70th anniversary of the World War Two "D-Day" landings in Normandy, his office announced on Wednesday, possibly creating an opportunity to talk.
French officials said Putin and Poroshenko would both attend a lunch on June 6 along with leaders including U.S. President Barack Obama, German Chancellor Angela Merkel and Polish President Bronisaw Komorowski, but could not confirm whether the two would meet.
While calling for an end to Kiev's military campaign, Putin has also announced the withdrawal of tens of thousands of Russian troops he had massed on the frontier. A NATO officer said on Wednesday thousands of Russian troops had indeed been pulled out, although tens of thousands were still in place.
In Berlin, Ukrainian Prime Minister Arseny Yatseniuk called on Moscow to stop rebels entering his country. "A number of trucks full of live ammunition, full of Russian-trained guerrillas crossed the Russian border into Ukraine," he said.
"We ask Russia and Putin to block the border to Ukraine ... If Russia is out of this game we can handle this situation in a week, but as they are supporting and financing them, and providing them access to Ukrainian territory, this creates huge difficulties for us."
Moscow denies that it is behind the rebellion.
FEAR AND DEFIANCE
In Donetsk, the main shopping mall remained closed for a third day and streets were mostly empty. The mayor, Oleksander Lukianchenko, renewed an appeal for people to stay at home and also reported some gunfire coming from the area of the airport.
Lukianchenko's municipal government has remained in place even as separatists have proclaimed themselves in power in the province, a sign of the confused loyalties in the area.
A young man in a helmet at the airport road barricade who gave his name as Yuri said: "I am doing what I can to help our fighters resist the advancing Ukrainian troops. They haven't slept for a third day now and are really nervous, expecting a renewed attack from Ukrainians at any moment."
Around 1,000 miners bussed in from around the eastern Donbass coalfield staged a demonstration in support of the separatists in Donetsk.
"Kiev does not rule us any more, we will no longer accept that," separatist leader Pushilin told the crowd. A Ukrainian fighter jet roared overhead and some gunfire could be heard in the distance, apparently from rebels in the vicinity of the security building shooting at the plane.
A miner from the state-owned Abakumova mine attending the demonstration who gave his name as Valery said: "I want peace and to be able to work and make money. I want the occupying soldiers to leave and return to their Kiev junta."
Russia and its state media which broadcast into eastern Ukraine have consistently described the government in Kiev, which took power after a pro-Russian president fled in February, as illegitimate and led by "fascists".
But Moscow's position was undermined by the scale of Poroshenko's election victory, and Kiev now appears emboldened to act with less threat of Russian retaliation.
Poroshenko, a former cabinet minister under both pro- and anti-Russian presidents, won 55 percent of the vote, preliminary results show, in a field of 21 candidates. He commanded support across the east-west divide that has defined Ukrainian politics since independence. His nearest challenger won just 13 percent.
The separatists blocked voting in Donetsk and neighbouring Luhansk provinces, but the 10 percent of voters kept away from the polls would not have made a difference to the final outcome.
Although many in eastern Ukraine are sceptical of the government in Kiev, opinion polls have shown most favour some sort of unity with Ukraine, despite referendums in Donetsk and Luhansk staged by the rebels on May 11 that recorded a vote for independence. The majority in the east describe themselves as ethnic Ukrainians who speak Russian as their primary language.
"We live in Ukraine," said Mikhail, 31, a theatre manager. "I work at the Ukrainian Theatre in Donetsk. Would I work at the Donetsk People's Republic Theatre? That doesn't sound so good. I think all this mess is only temporary.
"I didn't vote because we could not vote here, but Poroshenko seems decent," he said. "We will see. Many were elected as decent and then turned into bribetakers as a general rule. I hope he will not let Ukraine down."
