Officials said they are trying to work more closely with the private sector, including through deeper data collection and sharing solutions to attacks.
The meeting prepares the way for a summit at the level of presidents and prime ministers in Taormina, Sicily, on May 26-27.
Italy, which holds the G7's rotating presidency this year, pushed to make inclusive growth and economic inequalities a key topic.
While the administration says it is still considering some version of a border-adjusted tax, it doesn't plan to use the congressional proposal that spooked America's trade competitors.
The official, who asked not to be named or quoted directly, helped prepare the agenda for the Bari meeting.
"All the six others. said explicitly, and sometimes very directly, to the representatives of the USA administration that it is absolutely necessary to continue with the same spirit of global cooperation", French Finance Minister Michel Sapin told reporters.
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The area has been considered a de-conflicted zone under an agreement between the USA and Russian Federation earlier this month. The strike took place in At Tanf near Syria's border with Jordan and Iraq, the official said.
G7 finance chiefs vowed Saturday to unite against cyber crime as they wrapped up talks marked by signs of a thaw in the frosty relations between the United States administration and its main partners.
They also vowed to cooperate more against cyber crime, finance the global anti-terror fight, and promote a fair tax system including digital economy. Meanwhile, financial leaders warned the global recovery would still face various uncertainties.
"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.
But unlike a G7 leaders' communiqué of 2016, the Bari meeting did not endorse free trade and reject protectionism, reflecting pressure from the United States where President Donald Trump has signaled his skepticism about free trade deals.
Another focus of the meeting was cyber security.
"We recognise that cyber incidents represent a growing threat for our economies and that appropriate economy-wide policy responses are needed", said a statement issued at the end of their talks in southern Italy.
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The size [of the screen] should not be smaller than the chair on which you're sitting. So we need to pay attention", festival director Thierry Fremaux said in an interview.
Indeed, while the G7 made its pledge, a massive-scale cyber attack in private companies and public institutions was reported by nearly 100 countries in the world.
"The situations occurred in the past days and hours have proved once again the need of a common action", Italy's Padoan noted.
However, it seems this meeting will be another interesting opportunity for Germany to continue talks on tax.
"Protectionism has not been discussed neither explicitly nor implicitly", Padoan confirmed.
The final statement from the Bari meeting included a reference to "working to strengthen the contribution of trade to our economies", a word-for-word reproduction from March's G-20 in Baden-Baden, Germany.
The May 12 breakfast left some space for the Greek debt issue, ahead of the anticipated conclusion of the second review of the third bailout programme at the May 22 Eurogroup meeting.
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