It's the latest reaction to a French naval mission the the small uninhabited islands in January, when officers landed and painted the French flag on a rock.
In the the most scathing comments yet on the dispute, Mr Salwai said France had also disrespected Vanuatu's culture.
In a letter to French Prime President Emmanuel Macron, he said the government's priority was to see the return of Matthew and Hunter.
In comments reported by the Vanuatu Daily Post, Mr Salwai added that Vanuatu wanted a "friendly solution" to boundary issues with France.
The government is appealing to France, Fiji and the UK for assistance in resolving the issues, and not to take actions that would interfere with peace.
The Malvatumauri Council of Chiefs will hold a peaceful demonstration next week to express their concerns over the issues, President Chief Willie Grey Plasua told RNZ Pacific last week.