KYIV, Ukraine—Heavier shelling in a front-line Ukrainian region prompted officials to urge remaining civilians to evacuate Saturday as Russia stepped up attacks in Ukraine’s east ahead of an expected offensive.

Russia’s military was amassing forces and shelling was increasing in the east, making it more urgent for civilians in the area to leave, Serhiy Haidai, governor of the eastern Luhansk region, told Ukrainian public television.

The assault comes after a Russian missile strike Friday on the train station in Kramatorsk, to the west. The station was thronged with 4,000 Ukrainians heeding official calls to flee ahead of what both sides say is the next phase of the six-week-old conflict: a fresh Russian offensive to expand its hold on Ukraine’s east.

At least 52 people were killed and more than 100 were injured in the station attack, with five children among the dead and another 16 wounded as of late Friday, according to the head of the administration in the eastern region of Donetsk, where Kramatorsk is located.

Russia denied the strike but said its forces were targeting train stations to prevent Ukraine’s military from moving weapons and other supplies into the area, known as Donbas, which includes Donetsk and the neighboring Luhansk region. Ukrainian officials have accused Russia of thwarting evacuation attempts in the city of Mariupol and other parts of the country by mounting heavy artillery barrages.

Mr. Haidai, the Luhansk governor, said evacuations were being attempted via five corridors that were coming under attack.

“Every evacuation day is like the last,” Mr. Haidai said on social media. “The Russians do not allow for the protection of the lives of the inhabitants of the Luhansk region. Every day we take people out under heavy fire.”

Both sides are gearing up for a full-scale Russian assault in Donbas in the coming days, with Ukraine trying to remove civilians and send in military supplies while Russia repositions forces withdrawn from around Ukraine’s capital, Kyiv, in the north where they encountered stiff resistance.

Kyrylo Budanov, Ukraine’s head of military intelligence, said in an interview on CNN that the Russian forces that pulled out of northern Ukraine were regrouping across the border around the Russian city of Belgorod, where they are picking up additional troops to compensate for their losses.

A woman on a bus waved goodbye to her husband Saturday, a day after the attack on the train station in Kramatorsk.

Photo: fadel senna/Agence France-Presse/Getty Images

Mr. Budanov said the Kremlin’s renewed assault would attempt to take the northern city of Kharkiv and “try to finish off the city of Mariupol” in the south before advancing toward Kyiv.

Mr. Haidai said he expects the new Russian offensive to begin soon so that Moscow’s army could deliver “some kind of victory” ahead of May 9 commemorations of victory in World War II.

Friday’s train station strike on fleeing civilians came on the heels of allegations that Russian troops in their occupation of areas around Kyiv killed large numbers of civilians. Those alleged actions have further solidified Western support for Ukraine.

Ukrainian President Volodymyr Zelensky, in a televised address early Saturday, called the train-station strike the “latest war crime of Russia, for which everyone involved will be held accountable.” President Biden, U.K. Prime Minister Boris Johnson and others condemned the attack.

Mr. Johnson on Saturday became the latest European leader to travel to Kyiv to show support for Mr. Zelensky’s government. Mr. Johnson laid out a new package of military and other assistance “to support Ukraine in this crucial phase while Russia’s illegal assault continues,” his office said.

A damaged house after a rocket strike in Kharkiv, Ukraine.

Photo: THOMAS PETER/REUTERS

Bodies in bags at the site of a mass grave in Bucha, Ukraine.

Photo: Valeria Ferraro/Zuma Press

Included in the new aid, Mr. Johnson’s office said, are 120 armored vehicles and new antiship missile systems, which will come in addition to a package announced Friday of Starstreak antiaircraft missiles, 800 antitank missiles and high-tech munitions that loiter above targets for precision strikes.

European Commission President Ursula von der Leyen, who went to Kyiv on Friday, said after her visit that the European Union is proposing 500 million euros, equivalent to $544 million, in new support for Ukraine’s military, on top of 1 billion euros previously allocated for weapons.

“This war will be won on the battlefield,” EU Foreign-Policy Chief Josep Borrell, who accompanied Ms. von der Leyen, tweeted on Saturday.

As part of what he called his “to do list,” Mr. Borrell said that he planned to meet Sunday with the prosecutor of the International Criminal Court, who is investigating suspected war crimes in Ukraine.

Ukrainian authorities on Saturday continued collecting the dead and cleaning up in areas around Kyiv that had been occupied by Russian forces until their retreat in the final days of March.

A building destroyed by a Russian air raid in Borodyanka, near Kyiv.

Photo: Efrem Lukatsky/Associated Press

In the district of Makariv to the west of Kyiv, police traveled around villages picking up civilians who had been shot or died from shrapnel wounds or other causes. Officials said they had collected more than 100.

In Bucha, the Kyiv suburb where Russian forces left behind the bodies of several hundreds of civilians, people collected wreckage, piling it high on sidewalks and streets for removal. Cranes and dump trucks removing blackened and rusted Russian armored vehicles from a column the Ukrainian military had destroyed more than a month ago.

Government investigators questioned people about what they had seen during the occupation. Units with the town’s territorial defense searched homes whose residents they suspected of looting. The sounds of controlled explosions rocked Bucha now and then, as bomb technicians eliminated booby traps and unexploded ordnance.

Russia’s repositioning of its forces from northern Ukraine to the east provides a window for the West to supply Ukraine with more armaments, said Mr. Budanov, the military-intelligence chief.

“We are getting more supplies. These supplies are not enough,” Mr. Budanov told CNN. His list of needs includes heavy artillery, air-defense and missile systems, as well as combat planes, the latter of which the U.S. has been reluctant to provide out of concern it would bring it into direct conflict with Russia.

Mourners at a funeral in a village near Chernihiv, Ukraine.

Photo: Evgeniy Maloletka/Associated Press

Ahead of the expected offensive, Ukraine’s east—a site of persistent, mostly low-boil fighting since Russian-controlled separatists took over parts of the area in 2014—is becoming a war zone.

Ukrainian officials said Saturday that their forces held firm in the face of artillery barrages, some of which struck civilian buildings, and tank assaults in the past 24 hours.

Ukraine’s air-force command said that it intercepted a Russian drone, a cruise missile and a helicopter, and that the military in the eastern part of the country had downed a Russian helicopter.

Mr. Haidai, the Luhansk governor, said Russian forces had seized parts of the towns of Rubizhne and Popasna and were trying to push Ukrainian defenders out. In an interview with Ukrainska Pravda, a Ukrainian news portal, Mr. Haidai said that Russia had been hammering Popasna, a town of some 20,000, for more than a month, and that authorities were unable to organize the evacuation of civilians because of the intensity of strikes.

“They are destroying everything,” he said.

Mr. Haidai told public television that around 30% of residents remained in cities in the region, and he urged them to leave if possible.

Ukraine’s state railway company said 11 evacuation trains would depart Saturday from two cities in the country’s east to cities in the west.

The Black sea port city of Odessa, which has been repeatedly hit by missiles during the conflict, ordered a curfew from Saturday night to Monday morning over what the local military administration said is the danger of a missile strike.

The administration, in a Facebook post, specified Sunday as the timing for the possible attack. It didn’t provide further explanation but cited Friday’s missile attack on the Kramatorsk train station.

Write to James Marson at james.marson@wsj.com and Brett Forrest at brett.forrest@wsj.com