A Canadian ministry statement says Morneau and Mnuchin engaged in a "productive discussion" and that Canada committed to working out a durable solution of the issue.
U.S. Treasury Secretary Steven Mnuchin is due to explain Trump's plans to cut business taxes and regulation, and explain Trump's push for what he considers more balanced trading relationships.
A senior US Treasury official said Mnuchin had been quizzed on a series of issues, including Trump's tax-cutting plans.
Underscoring the cybersecurity threats, G-7 officials pointed to a massive attack that scrambled computer systems in dozens of countries on Friday.
Trump has proposed slashing the US corporate income tax rate and offer multinational businesses a steep tax break on overseas profits brought back home.
Mnuchin, who skipped the opening session in Bari where academics spoke on inequality and growth and arrived long after other ministers, told reporters he was "excited" about the emerging new USA trade policy. Trump has vowed to press for trade that is fair as well as open and benefits USA workers and has focused on bilateral, or country-to-country, relations.
Already, Trump has yanked the United States out of the 12-nation Trans Pacific trade agreement and threatened to pull out of its NAFTA agreement with Canada and Mexico. The Organization for Economic Cooperation and Development, a group representing many advanced economies, has urged the U.S.to lower its corporate tax rate.
Whilst the final communique included some wording referring to fighting inequality and financial inclusiveness of the global economy as a desirable target, Mnuchin's view of a better model of worldwide trade as rather "fair" instead of "free" prevented a G7 consensus on the matter. But he offered little detail.
Italian Finance Minister Pier Carlo Padoan said that Saturday's morning session on cybercrime was "unfortunately very timely", an apparent reference to the wave of ransomware attacks reported Friday in dozens of countries in which files were locked and money demanded to unlock them.
The closing statement from Bari will reiterate a warning against competitive devaluations, Italian officials said, as March's G20 did, allaying fears that the new U.S. administration might weaken the G20's united front on global currency policy.
According to French Finance Minister Michel Sapin, all the other rich countries unanimously called on U.S. to respect global trade.
The meeting also coincided with news of a significant foray by the Trump administration into global commerce.
Today's meeting in the southern Italian town Bari is paving the way for a meeting between the G-7 leaders in Taormina, Sicily in May 26-27.
Besides ministers and governors from the Group of Seven - comprising Canada, the U.S., France, Germany, Italy, Britain, and Japan, top officials from the European Union (EU) and the International Monetary Fund (IMF) also joined the meeting.