During the visit to the front near Bakhmut, Zelensky recognized his troops had a "difficult" task.
Russian forces have posted steady gains towards capturing Bakhmut in recent months.
The Crimean Peninsula seized by Russia from Ukraine, has been hit by a series of Ukraine drone attacks.
President Volodymyr Zelensky on Wednesday visited military positions near the frontline town of Bakhmut in Eastern Ukraine, as a Russian strike battered a nearby residential building injuring dozens.
“At least one person was killed and 32 more injured in the block of flats in Zaporizhzhia, a city near the frontline, just before Zelensky announced his visit to the front,” the mayor said.
Ukraine officials further announced the death toll from a separate overnight drone attack by Russia on a school south of the capital Kyiv had risen to seven, with another nine injured.
During the visit to the front near Bakhmut, a town experiencing the longest and bloodiest battle of Russia's invasion, Zelensky recognized the troops had a "difficult" task.
"I am honoured to be here today to award our heroes. To shake hands and thank them for protecting the sovereignty of our country."
Video released by Zelensky's office showed him meeting servicemen in a warehouse and handing out state decorations.
ICC rejects Russian threats
Russian and Ukrainian forces have invested heavily in the battle for Bakhmut, even though analysts say the city carries little strategic value.
Kyiv says the battle for the industrial town, which had a pre-war population of around 80,000 people, is key to holding back Russian forces along the entire eastern front.
As the battle grinds on, the International Criminal Court (ICC) rejected threats reportedly made against the court by a key ally of President Vladimir Putin after it issued a war crime warrant against the Russian leader.
According to Dutch media, former Russian president Dmitry Medvedev reportedly talked about targeting The Hague, where ICC is based, with a hypersonic missile as a reprisal for the Putin warrant.
The presidency of the Assembly of States Parties, which groups the ICC's 123 member countries, said it shames these attempts to hinder international efforts to ensure accountability for acts that are prohibited under general international law.
Russian gains
Russian forces have posted steady gains towards capturing Bakhmut in recent months.
In the heavily bombarded eastern town of Chasiv Yar, AFP journalists saw convoys of tanks and armoured personnel carriers speeding along the road to and from Bakhmut.
Soldiers taking a break from the front were sheltering in cellars, while one soldier smoked near a block of flats.
He said his team were having a "chill day" despite the explosions nearby, as they rested after Bakhmut.
"There is a lot livelier than here. Our company was withdrawn so we can have a day to get washed and await orders," he told AFP.
An aide to the Russian-appointed head of the Eastern Donetsk region in Ukraine on Wednesday said that Moscow's forces were close to cutting off Kyiv's road links to the city.
Yevgeny Prigozhin, the head of Russia's Wagner mercenary group, which claims to be spearheading Moscow's offensive for the city, said this week that his forces control some 70 percent of Bakhmut.
Zelensky also distributed images of the strike on Zaporizhzhia, showing a projectile smashing into the residential building and a large plume of black smoke rising.
"We will certainly respond to every blow of the occupier on our cities," he said, citing Russian strikes on Zaporizhzhia and the night attack on the Kyiv region.
Russia repels drone attacks
Artem Mayboroda, a 16-year-old Zaporizhzhia resident, told AFP he began dressing when the strikes shook his sixth-floor apartment.
"Everything began to crumble and fall as I rushed downstairs. There is neither apartment nor balcony. The fire engulfed our apartment," he said.
That attack came hours after seven people were left dead in a Russian drone attack on a school about 80 kilometres (50 miles) south of Kyiv.
“An ambulance driver called to the scene was among those killed,” the office of Ukraine's prosecutor general said.
And meanwhile Moscow said it had "repelled" a drone attack by Ukraine targeting the Crimean port city of Sevastopol.
The Crimean Peninsula, seized by Russia from Ukraine in 2014, is home to Moscow's Black Sea Fleet and has been hit by a series of drone attacks since Russia invaded Ukraine.
Russian Defence Minister Sergei Shoigu said two women who shot down two of the three drones, would be awarded and given cash bonuses.
‘Serious’ escalation
Also in Moscow, Russia’s Foreign Minister Sergei Lavrov warned Britain over its plan to supply Ukraine with armour-piercing ammunition containing depleted uranium.
"This is a step towards a further escalation and a serious one at that," Lavrov said.
The United States dismissed Russia's complaints, with White House National Security Council spokesman John Kirby saying the ammunition was "a commonplace type of munition".