AFP journalists on April 2 last year discovered the bodies of at least 20 people in civilian clothing, some with their hands tied behind their backs, lying in a street of the suburb.
Zelensky said Bucha had become "a symbol of the atrocities" committed by Russian forces, who have been linked to the extra-judicial killings of unarmed civilians in Bucha.
"We will never forgive. We will punish every perpetrator," Zelensky said in a statement on social media.
During a visit to Bucha days the Russian troops' withdrawal, Zelensky described the killings as "genocide".
Ukraine and its Western allies have accused Russian troops of war crimes after the discoveries, pointing to an abundance of footage and witness accounts.
Prosecutors in Kyiv say Russian forces killed some 1,400 civilians around Bucha and that they have identified dozens of Russian soldiers responsible.
But Moscow denies the accusations, claiming the atrocities in Bucha were staged.
Many foreign leaders and officials who have visited Ukraine since the war started have made a stop in Bucha.
'Continue to live'
Japanese Prime Minister Fumio Kishida said he had a "strong sentiment of indignation" in Bucha last week.
After Russia withdrew from near Kyiv, fighting shifted to the south and east of Ukraine, with the embattled city of Bakhmut now the scene of the longest and bloodiest battle since the invasion.
But a year after it was retaken by Kyiv's forces, Bucha has not forgotten its victims.
The community of the suburb is rebuilding, and locals told AFP "the pain subsides" and that they must "continue to live".
AFP on Thursday saw dozens of construction workers weaving between diggers and trucks, as they worked to rebuild homes and roads in the town, which had a pre-war population of some 37,000 people.
Archpriest Andriy, who runs the local parish, said it is "important" not to forget those who are "not with us today".
"But it is also important for us not to live in the past but in the future," he told AFP.
In the weeks following Russia's withdrawal from other towns near Kyiv, hundreds more bodies were found in homes, basements and shallow graves across the north.
Ukraine wants to establish a special tribunal to prosecute Russia's leaders but there are complex legal disputes over how it could work.
The International Criminal Court earlier this month issued an arrest warrant for Putin over the unlawful deportation of children from Ukraine.
Chief ICC Prosecutor Karim Khan has described Ukraine as a "crime scene".
Russia has repeatedly denied any abuses by its forces, and foreign ministry spokeswoman Maria Zakharova this week described scenes in Bucha as a "crude and cynical provocation" by Kyiv.
© Agence France-Presse