The talks came after Putin warned he could pull the plug on crucial Russian gas supplies to Western Europe this winter.
EU leaders also attended the breakfast meeting at the Milan prefecture building, held amid very sharp differences with Moscow over implementation of a ceasefire and peace accord agreed last month between Kiev and pro-Russian rebels.
Ukrainian President Petro Poroshenko said he hoped the breakfast meeting with the Russian leader would help shore up a patchy ceasefire between his government forces and pro-Moscow rebels in the east of Ukraine.
"Peace and stability in Ukraine, it is the only thing we expect," Poroshenko told reporters late on Thursday after talks with Angela Merkel.
The German Chancellor went to have a late night meeting with Putin, who on Thursday upped the stakes in his confrontation with the West by warning that the flow of Russian gas to EU countries could face "major transit difficulties" this winter.
The diplomatic shuttling over Ukraine is taking place on the sidelines of an Asia-Europe (ASEM) summit that has been completely overshadowed by the crisis, which has deepened in recent days.
NATO said it had seen no sign of any major Russian pullback from the Ukrainian border despite Putin saying earlier this week nearly 18,000 troops had been withdrawn from the frontier.
US and European Union leaders had welcomed that announcement as a positive gesture ahead of the Poroshenko talks but also reminded Putin that sanctions would remain in place until he stopped meddling in Ukraine completely.
With the financial markets in turmoil, partly due to the uncertainties over Ukraine, Merkel had earlier tried to put the ball firmly in Putin's court.
Merkel said it was "first and foremost" Russia's responsibility to make sure a ceasefire and peace plan agreed last month with the rebels "really will be implemented."
Merkel, French President Francois Hollande, British Premier David Cameron and Italian leader Matteo Renzi are all due to sit in on the Putin-Poroshenko meeting.
"It will be an opportunity to deliver a collective message that Putin has to start real peace negotiations," said an aide to Hollande.
Friday's meeting was always expected to be difficult and the latest exchanges appear to make that more likely.
Putin has this week accused US President Barack Obama of outright hostility towards Russia and insisted he would not be blackmailed by the West.
The Russian president has also played his gas trump card, effectively reminding Europe that it gets about a third of its supplies from Russia.
Putin insisted he did not want to see a repeat of 2006 and 2009 when interruptions of supplies to Ukraine disrupted onward deliveries to Europe which gets about a third of its gas from Russia.
"I am very much hoping that it will not come to that," Putin said.