The Vatican, however, did not address the latter issue in its statement, focusing instead on the humanitarian and political situation in Ukraine caused by the war.
In a tweet, Mr Zelenskyy noted significant political decisions made to increase aid for Ukraine during his visit.
He highlighted a joint declaration concerning Ukraine's potential accession to the EU and Nato, symbolising Italy's explicit support for the Ukrainian Peace Formula.
Mr Zelenskyy also expressed hope for the potential impact of his conversation with Pope Francis, specifically regarding the return of displaced Ukrainian children.
During his visit to Rome, Mr Zelenskyy also received assurances of continued military, financial, and humanitarian support from Italian officials, including President Sergio Mattarella and Prime Minister Giorgia Meloni.
Italy has contributed about €1 billion in aid since the war began.
Mr Zelenskyy's 10-point peace plan includes the establishment of a special tribunal to prosecute Russian war crimes, the restoration of Ukraine's damaged power infrastructure, and the creation of a European-Atlantic security architecture with guarantees for Ukraine.
The Ukrainian leader's visit to Rome comes amid continuing hostilities, with reports of missile strikes and military crashes in Ukraine, and an additional €2.7 billion ($3 billion) military aid package from Germany.
Italy's preparation for the visit
Large areas of the Italian capital were locked down in preparation for Mr Zelenskyy's, before meetings with Pope Francis, Italian President Sergio Mattarella and Prime Minister Giorgia Meloni.
On his first visit to Italy, Mr Zelenskyy was greeted at Ciampino Airport in Rome airport by Italy's Foreign Minister Antonio Tajani.
“We renew our commitment by the side of Ukrainian people, in defence of freedom and democracy,” Mr Tajani said.
“Italy welcomes Ukraine President Volodymyr Zelenskyy.”
Mr Zelenskyy started his day of official engagements with a meeting at Quirinale Palace with President Mattarella.
“We are fully at your side,″ Mr Mattarella said to Mr Zelenskyy shortly after he arrived. It's thought that Mr Mattarella reiterated Italian support for Ukraine, both militarily and financially.
Since the Russian invasion, Italy has provided Ukraine with around a billion euros ($1.1 billion) in military and financial assistance.
Then it was on to the office of the prime minister, where Mr Zelenskyy had a closed-doors meeting with Ms Meloni.
Ms Meloni had met before Mr Zelenskyy in February, when she went to Kyiv to show Italy's support for Ukraine.
She also welcomed Ukraine's Prime Minister Denys Shmyhal to Rome in April during a conference on how Italian businesses could help rebuild the war-torn country.
The visit comes as Germany announced on Saturday that it is preparing a new weapons package for Ukraine worth €2.7 billion ($3 billion).
“We all hope for a rapid end to this terrible war by Russia against the Ukrainian people, but unfortunately this is not in sight,” Defence Minister Boris Pistorius said.
“This is why Germany will supply all the help that it can, for as long as necessary.”
The package will include 30 additional Leopard-1 tanks, Marder armoured vehicles, air-defence systems and surveillance drones, the ministry said.
It has been mooted that Mr Zelenskyy will travel to Berlin following his meetings in Rome.
Western allies have delivered increasingly powerful and sophisticated weapons to Ukraine since the Russian invasion of February 2022, including Storm Shadow missiles from the UK.
Russia described the UK move as “an extremely hostile step” and on Saturday accused Kyiv of using them to target civilian sites in eastern Ukraine.
EU foreign policy chief Josep Borrell said other European nations should provide similar long-range weapons.
“The Russians are bombing from far away so the Ukrainians have to have the capacity to reach … the same distance, the same range,” he said on Saturday, following a meeting with Ukraine's Foreign Minister Dmytro Kuleba in Stockholm.
Mr Zelenskyy's long-standing request for advanced fighter jets has so far not been met.
On the frontline
In Ukraine itself, there have been reports of increased fighting in the front-line city of Bakhmut, with Kyiv said to be about to launch a spring counter-offensive.
Senior Ukrainian military commander Oleksandr Syrskyi said on social media that Kyiv's forces were advancing in Bakhmut and that “the enemy is losing equipment and manpower”.
But Russia said its forces were still progressing in the city.
“In the Donetsk direction, assault detachments liberated a block in the north-western part of the city of Artemovsk,” the Defence Ministry said, referring to Bakhmut by its Russian name.