German Finance Minister Christian Lindner speaks to the press with French Economy and Finance Minister (unseen) about Russia s invasion of Ukraine at the Economy Ministry in Paris on February 25, 2022, prior to the start of an informal Ecofin and Eurogroup meeting. AFP
SWIFT's messaging system allows banks to communicate rapidly and securely about transactions, and cutting Russia off would cripple its trade with most of the world.
Germany had been more cautious about excluding Russia from SWIFT. Russian gas makes up a higher share of its energy supplies than other European countries.
But Foreign Minister Annalena Baerbock and Economy Minister Robert Habeck said they were working "urgently on limiting the collateral damage from an exclusion from SWIFT so that (the measure) hits the right people".
"What we need is a targeted and functional limitation of SWIFT," they added in a joint statement.
Zelensky had earlier urged the European Union to impose the sanction and called out Germany and Hungary, as troops battled for Ukraine's capital Kyiv.
"There is already almost full support from the EU countries to disconnect Russia from SWIFT. I hope that Germany and Hungary will have the courage to support this decision," Zelensky said in a video address posted online.
The Hungarian government angrily denied suggestions it had blocked moves to exclude Russia from SWIFT.
Foreign Minister Peter Szijjarto said on Facebook that such claims were "fake news".
"We have never spoken out against a single sanction proposal, we have not blocked and are not blocking anything," he said.
Government spokesman Zoltan Kovacs further tweeted that "Hungary stands 100 percent in alignment with the joint EU effort.
"We're doing no less than what the EU position calls for. And it's not dependent on Hungary to do more," he added.
However, neither statement explicitly clarified whether Budapest was in favour of the move.
Cutting off Russia from SWIFT could complicate remaining trade with Europe.
Ahead of a meeting with German Chancellor Olaf Scholz, Polish Prime Minister Mateusz Morawiecki had criticised the "unyielding egoism that we see in certain Western countries, including here in Germany".
He urged Berlin to "finally decide on sanctions that are actually crushing", including the exclusion from SWIFT.
Earlier this week German Finance Minister Christian Lindner said he was "open" to including SWIFT in the EU's sanctions response package.
But he added that it "would mean that there is a high risk that Germany will no longer receive gas, raw material supplies from Russia".
Italy has also been reluctant to exclude Russia from SWIFT over fears Moscow could cut off gas supplies.
Italian Prime Minster Mario Draghi spoke to Zelensky on Saturday and "reaffirmed... that Italy will fully support the EU line on sanctions against Russia, including those relating to SWIFT", according to an Italian government statement released after the phone call.
Iran has been disconnected from the SWIFT system in the past over its nuclear programme.
Russia meanwhile has been developing domestic financial infrastructure to counter such a threat, including the SPFS system for bank transfers and the Mir card payments system.