"An important visit for (the) approaching victory of Ukraine!" Zelensky tweeted as he arrived in Rome, on his first visit to EU and NATO member Italy since Russia invaded Ukraine in February 2022.
Zelensky was due to travel on Sunday to Berlin, a German government source said, where the defence ministry earlier Saturday announced a new weapons package worth 2.7 billion euros ($2.95 billion) for Ukraine.
There was a heavy security presence in Rome for Zelensky's visit, which began with a formal welcome by President Sergio Mattarella, followed by a 70-minute face-to-face with Meloni.
In a joint press conference, Zelensky thanked Meloni "for helping to save lives" while detailing what he called fresh aggressions by Russia.
"I have not come to complain, I have come to talk about our cooperation and to thank you once again for helping us, for the sake of our country, because we want peace," he said.
Despite a history of warm ties with Moscow, including within Meloni's hard-right coalition government, Italy has been a strong supporter of Kyiv, sending weapons and aid and backing sanctions against Russia.
Meloni, who visited Zelensky in Kyiv in February, added: "I am convinced that Ukraine will win and be reborn stronger, more proud and more prosperous than before."
Zelensky then headed straight to the Vatican for a meeting with Pope Francis, which he described as a "great honour", according to footage released by the Holy See.
The 86-year-old pontiff has repeatedly called for peace in Ukraine and prays for the victims of the war almost every week, although his offers to mediate have yet to yield any public results.
Russia "bound to lose"
The new package from Germany, which will include 30 additional Leopard-1 tanks, Marder armoured vehicles, air-defence systems and surveillance drones, is reportedly Berlin's largest since Russia's invasion.
"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 in a statement.
"This is why Germany will supply all the help that it can, for as long as necessary," he said.
Mykhailo Podolyak, an adviser to Zelensky, hailed the announcement, saying it indicated that Russia was "bound to lose and sit on the bench of historical shame."
Western allies have delivered increasingly powerful weapons to Ukraine, and Britain this week announced it was sending Storm Shadow missiles, becoming the first country to send longer-range arms to Kyiv.
Russia described it as "an extremely hostile step" and on Saturday accused Kyiv of using the British missiles to target civilian sites in eastern Ukraine, and wounding six children.
But EU foreign policy chief Josep Borrell on Saturday urged other European nations to provide long-range weapons for Ukraine, while accelerating arms deliveries overall.
"The Russians are bombing from far away so the Ukrainians have to have the capacity to reach... the same distance, the same range," Borrell said after a meeting with Ukraine's Foreign Minister Dmytro Kuleba in Stockholm.
"But we have to speed up," he said.
On the front line, meanwhile, near the eastern flashpoint town of Bakhmut, both sides claimed to be making progress.
"Our soldiers are moving forward in some areas of the front, and the enemy is losing equipment and manpower," commander of the Ukrainian ground forces Oleksandr Syrskyi said on social media.
Russia said its forces were still pushing inside Bakhmut.
"In the Donetsk direction, assault detachments liberated a block in the northwestern part of the city of Artemovsk," the defence ministry said, referring to Bakhmut by its Russian name.
The conflicting reports from the battlefront suggest an increase in fighting after months of relative stability, as expectations grow over Kyiv's spring counteroffensive.
The question of when and where Ukraine might launch its high stakes battle to push Russian forces from occupied land has been the subject of steady speculation, although Zelensky insisted earlier this week that his army needed more time to prepare.
Suffering and death
Pope Francis last held an audience with Zelensky in February 2020, but they have spoken on the phone since Russia invaded.
During an address to ambassadors earlier Saturday, the pontiff again lamented the conflict in Ukraine that he said "has brought suffering and unspeakable deaths".
During a papal audience last month, Ukrainian Prime Minister Denys Shmyhal invited the pope to Ukraine and asked for his help in returning children forcibly taken to Russia.