Fighting has intensified in eastern Ukraine after the president, Petro Poroshenko, announced an end to a ceasefire and said he was ordering his forces to attack pro-Russian separatists.

In a televised address on Monday night, Poroshenko said the 10-day ceasefire had ended, and vowed that Ukrainian government forces would "attack and liberate our land".

Clashes were reported around both the Donetsk and Lugansk regions on Tuesday morning. Four people were killed and five wounded when a small bus came under fire in Kramatorsk, local news outlets reported. Photographs from the scene showed a woman's body lying in the aisle amid broken glass and blood.

Other images published by InfoResist, an analytical group with close ties to the Kiev government, showed gaping holes and destroyed balconies in several residential buildings in Kramatorsk.

Local resident Alexei Sergeyev said he heard periodic shooting and explosions throughout the night, including near the airfield that Ukrainian forces have been using as a staging ground. Sergeyev said he was fleeing the city on Tuesday morning along with many other residents.

"Around 8pm they started shooting from something big, maybe a mortar, maybe a tank, and then during the night there was heavy machine gun firing. It was intense, the windows were shaking," Sergeyev said.

The idea behind the truce – which was announced on 20 June – was to give pro-Russian rebels a chance to disarm and to start a broader peace process including an amnesty and new elections.

But the ceasefire has been repeatedly breached since Poroshenko declared it, with both sides blaming the other. In his address on Monday night, Poroshenko accused the rebels of breaching the ceasefire more than 100 times.

"Peace is, was and will be my goal," he said. "Only the instruments of achieving it are changing … The defence of Ukraine's territorial integrity, of the security and lives of peaceful citizens, demands not just defensive but offensive action against the terrorist militants."

Ukraine map

An aide to Ukraine's interior minister posted on Facebook that rebels had begun surrendering in some areas of Kiev's "anti-terrorist operation", and the newspaper Ukrainskaya Pravda reported that some rebels were asking for a corridor to put down their arms and leave areas surrounded by government forces.

The spokesman for Alexander Borodai, the prime minister of the self-declared Donetsk People's Republic, said he did not know of any such instances. He confirmed reports of firefights in the city of Donetsk but declined to provide further details. Neither report could be confirmed.

A Twitter account of the self-declared Donetsk People's Republic denied reports that a tank battle was taking place in the city of Karlovka. Instead, it said government forces had fired Grad rockets at rebel positions. Nato satellite images suggested three tanks came across the border from Russia last month, and Donetsk and Lugansk leaders have both said they have tanks.

There were also reports of fighting in the Lugansk region near the Russian border on Tuesday. The Russian television channel REN-TV reported that one of its cameramen was wounded at the Izvarino crossing when a howitzer shell landed nearby, the latest casualty among the Russian press after a Channel One cameraman was killed by Ukrainian gunfire on Sunday night.

Igor Strelkov, the Russian commander of rebels in the besieged city of Slavyansk, was quoted by pro-Russian bloggers as saying that many civilians had been wounded after government forces shelled several villages around the city overnight. He said rebels had not sustained any losses.

Poroshenko's decision followed four-way talks in search of a solution with Russia's president, Vladimir Putin, the German chancellor, Angela Merkel, and the French president, Francois Hollande, on Monday as the deadline approached. He issued a statement after the talks ended, saying the key conditions needed to continue the ceasefire had not been met.

On Tuesday, Russia urged Kiev to reinstate the ceasefire. "We demand that the Ukrainian authorities refrain from shelling civilian cities and villages in their own country, return to a real, not a fake, ceasefire to safeguard the lives of the people," the Russian foreign ministry said in a statement.

European leaders and the US have urged Russia to use its influence with the rebels to ease the bloodshed and have threatened to impose another round of economic sanctions against Moscow.

While Putin has expressed support for the ceasefire, the west has accused Russia of sending weapons and fighters across the border into Ukraine. Moscow says any Russians in Ukraine have gone there as private citizens.

Tension between Russia and Ukraine escalated in February when protests by people who wanted closer ties with the European Union drove the pro-Russia president Viktor Yanukovych from office. Russia called that an illegal coup and seized Ukraine's Crimea region, saying it was protecting the rights of people there who speak Russian as their main language.

The insurrection in the eastern regions near the Russian border started soon afterwards, with separatists occupying buildings and declaring independence.

The end of the ceasefire raises the question of what action the Ukrainian military can take. It has been unable to dislodge rebels occupying the city of Slovyansk or to retake control of three key border crossings with Russia. At one point, the rebels shot down a government military transport, killing 49 service members.