"Finding in the Holy Father confirmation of the readiness to host the next talks between the parties in the Vatican, the prime minister expressed deep gratitude (to) Pope Leo XIV for his unceasing commitment to peace," Meloni said.
Following a call on Monday between US President Donald Trump and Russia's leader Vladimir Putin, Meloni's office said she welcomed remarks by Trump that Leo had expressed an interest in hosting talks between Ukraine and Russia but the Vatican did not immediately confirm any such offer.
Pope Leo, elected two weeks ago, is the first US leader of the global Catholic Church.
In a May 14 speech, he said the Vatican could act as a mediator in global conflicts, without specifically mentioning of Ukraine and Russia.
In a second, separate statement the Italian prime minister said she also had talks with other European leaders and with Ukrainian President Volodymyr Zelenskiy over the next steps.
"It was agreed to maintain close co-ordination between the partners with a view to a new round of negotiations aimed at a ceasefire and a peace agreement in Ukraine," the statement said.
Meanwhile, Ukrainian authorities on Tuesday said they have begun evacuating more than 200 locations in the Sumy region near the border with Russia.
So far, 52,000 people have been brought to safety, Sumy's military governor, Oleh Hryhorov, said on Ukrainian television on Tuesday.
He said that this accounts for 60 per cent of the total 86,000 civilians subject to relocation in the settlements.
"We ensure transport, accommodation, as well as humanitarian, financial and psychological assistance," Hryhorov said.
He did not specify when the relocation is expected to be completed.
The Sumy region has been the site of heavy Russian attacks for months.
with DPA