The focus on cyber crime followed a globe-spanning wave of cyber attacks that hit computer systems in nearly 100 countries on Friday, notably disrupting Britain's health service and bringing production at carmaker Renault to a standstill in France.
The ministers said in a statement that cyber incidents represent a growing threat to their economies and that tackling them should be a priority.
"We know nothing about it but of course we want to know how they hacked into very secure systems," said Ignazio Visco, governor of the Bank of Italy.
"At the moment it seems not to have created any problems for the financial system."
Italian finance minister Pier Carlo Padoan joked that the attacks had been perfectly timed.
"We tried to convince everyone we organised it to show how important the Italian agenda is," he quipped at the end of two days of discussions in a Norman fortress on Italy's southern Adriatic coast.
The isue has been on the agenda of the G7 for some time, with the primary focus on the potential threat of hackers being able to infiltrate the computer systems that run the international banking system, capital and equity markets.
Trump tax cuts
In concrete terms, the ministers mandated experts to continue their work on assessing the nature of the threat. Padoan said progress would be reviewed again when G7 leaders, including Donald Trump and new French President Emmanuel Macron, meet in Sicily at the end of this month.
Differences between the Trump administration and the rest of the G7 on free trade, the importance of multilateral institutions and climate change were again sidestepped, as they were at the G20 meeting in Germany earlier in the year.
But participants in the talks said relations with the US team led by Treasury Secretary Steven Mnuchin, making his G7 debut, were improving as familiarity breeds mutual confidence.
"With Steven Mnuchin, our relations are improving every time we meet," Padoan said.
"Of course there are differences and divergences ... but we are working well together on common areas of concern and joint measures."
Mnuchin said he "couldn't be happier with the last two days."
He felt people were becoming "more comfortable" with the goals of the new administration and said there had been much interest in Trump's plans to slash taxes.
Padoan said Mnuchin had told them tax reform would be "neither short nor simple" in light of opposition in Congress.
"People have a level of understanding of Trump's policies," Mnuchin said. "On the trade side, our objective is to grow exports, to give more opportunities to American workers to make things and sell them."
'Trade not free, fair'
Officials from the big European economies, Canada and Japan remain concerned about a lack of visibility over how Trump plans to implement his 'America First' agenda.
On that score, several senior European officials said they had been reassured by news of a new US-China trade deal, which they interpreted as a sign of flexibility and pragmatism on the part of the new administration, potentially suggesting fears of a new era of protectionism had been overstated.
"It is an encouraging sign," Padoan said.
In his first comment on the trade deal's substance, Mnuchin hailed the opening of China's beef market as "a big deal for US farmers."
"We don't want to be protectionist but we reserve the right to be. We believe trade is not free and fair."
On the global economy, the ministers noted that recovery was gaining momentum but that output remains below potential in many countries "with the balance of risks tilted to the downside".
There were also important discussions on the sidelines of the meeting about debt relief for Greece.
Talks between the leadership of the IMF and Eurozone lenders did not wrap up a deal to proceed with a new bailout package for the debt-plagued country.
But a green light for the 86-billion-euro package, the third international rescue of the Greek economy since 2010, is now expected to be issued on May 22, potentially bringing an end to the painful cycle of austerity Greece has endured for a decade.
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