In a joint statement, the G7 ministers called particularly on countries in conflict situations "to identify and ban the trade in stolen cultural artefacts."
The meeting in the culturally rich Italian city of Florence was the first of its kind for the G7 grouping and the brainchild of Italian Culture Minister Dario Franceschini.
"It is vital that the G7 nations play an important role at the heart of the international community, not only economically but also through their values, their ideas, their principles," said Franceschini, hosting his counterparts from Britain, Canada, France, Germany, Japan and the United States.
Britain's Culture Minister Karen Bradley thanked her G7 colleagues for their solidarity following the deadly attack in Westminster last week.
On the issue of the trafficking of cultural items she said: "There is an urgent need for action".
"We are witnessing looting and vandalism on a heart-breaking scale. Not only do these assaults help finance terrorism, they are a calculated attempt to destroy people's history, culture, and identity."
Ahead of the talks Franceschini said "because of the importance of our own heritage, Italy has a leadership role in issues of culture".
"We want to translate this strength into action at the international level by putting the idea of cultural diplomacy onto countries' agenda."
He added that the recent damage inflicted on Roman-era monuments in the Syrian city of Palmyra had raised public awareness of the importance of the issue.
The meeting is part of the preparations for a summit of the leaders of the G7 countries in Sicily at the end of May.
Also taking part in the meeting was EU Culture Commissioner Tibor Navracsics and Irina Bokova, head of the UN cultural body Unesco.
"We need still more political will to put culture at the centre of the international agenda," Bokova said.