The meeting with Ukraine's president was one of several encounters with world leaders by the prime minister while on the sidelines of Pope Leo XIV's inauguration at the Vatican.
Mr Albanese also held a one-on-one meeting with European Union President Ursula von der Leyen, who raised the prospect of closer defence agreements between the EU and Australia.
The prime minister told Mr Zelenskiy Australia would provide more military equipment to Ukraine as it battles with Russia's invasion.
"We have tanks that are on their way at the moment, which is a very positive initiative," Mr Albanese said during the meeting.
"The Russian illegal aggression needs to be resisted and we stand with Ukraine very clearly and unequivocally, and we also have, of course, called for peace."
The Ukrainian president also called for more sanctions to be placed on Russia by countries such as Australia to maintain pressure on Moscow.
While on the sidelines of the papal inauguration, Mr Albanese also spoke with Canadian Prime Minister Mark Carney, German Chancellor Friedrich Merz and UK Deputy Prime Minister Angela Rayner.
However, Mr Albanese did not have a one-on-one meeting with US Vice President JD Vance, who also attended the inauguration.
He did get the opportunity to speak with Pope Leo XIV following his inauguration, which Mr Albanese said was a "warm discussion".
The conversation took place after a number of world leaders were taken into the basilica to greet the Pope after the mass.
"I spoke to him about my mother who would be, I'm sure, looking down from Heaven with the biggest smile she's ever had," Mr Albanese said.
"The fact that her son was at the inaugural Mass of a Pope in the Vatican, was quite extraordinary.
"So, for me it was a very personal moment as well, and it was a personal discussion."
Mr Albanese, who was raised Catholic in a housing commission flat in Sydney, often references his single-parent mother and her influence on his life.
Security ties were brought up during the discussions with the EU's president after the inauguration, with Ms von der Leyen raising the idea of defence agreements between Australia and the trading bloc, similar to arrangements it already has with Japan and South Korea.
Mr Albanese said Australia had defence agreements in place with EU countries such as Germany, but would consider Ms von der Leyen's proposal.
"We said that we were certainly interested in any further engagement of support. But it's very early stages at this point," he told reporters in Rome.
"There was no detail further, just it was really an assertion of Europe's values being consistent with Australia's values."
The discussions with Ms von der Leyen come as Australia is trying to carve out a trade agreement with the EU.
Federal frontbencher Tanya Plibersek agreed there had been a few "sticking points".
"There's about a thousand names that the European Union wants to restrict the use of, and they are parmesan, fetta, prosecco, a whole lot of names of food that are related to the place where they come from," she told Seven's Sunrise program.
A trade agreement with the EU would open up a huge market for Australian goods and services.
As a bloc, the EU was Australia's third-largest two-way trading partner in 2022/23. It's also the sixth-largest export destination and the third-largest services export market.
Two-way trade is valued at around $110 billion.
