The first lease for about 16,500 sq ft (1,532 sq m) of space in the first of six buildings has been signed.
Senator Alan Maclean said protests and petitions made it harder to get firms to sign a lease.
A petition against the development by the Jersey Development Company currently has about 1,000 signatures.
Banking group UBS is the first firm to sign a pre-let agreement for office space on the former Esplanade car park site.
The land is owned by the States of Jersey and the development is being completed by government owned body The Jersey Development Company (JDC).
Senator Maclean said a lot of misinformation had been spread and even though Swiss bank UBS had signed up for about a third of one building, it was enough to guarantee a profit.
He said it was too late to stop the development as more than Â£5m had been spent by the JDC to get to this point in the development.
The minister said: "It is bad enough seeing front page articles talking about protests against the finance centre with thousands of people.
"That gets picked up internationally. What sort of impression does that give of this island as a whole? It does no good for any of us.
"We have been through a process to get to this point, lets get behind the development company, celebrate UBS signing up and get a move on with this."
Deputy Montfort Tadier, of Reform Jersey, who called for a referendum on the development before any work began, said it had previously been promised no work would start until 200,000 sq ft (18,581 sq m) had been let.
He said: "It would seem that the democratic process is an irritant to the oligarchs who are increasingly running our island.
"The minister should get his own house in order and stop breaking promises which were made by his predecessor which were taken by the Assembly in good faith."
Senator Maclean said the promise applied to the previous developer, Harcourt, and that ended when the Jersey Development Company took over.
Further public meetings are to be held to explain what the JDC is planning to build on the Esplanade car park.
Continued debate and protest over the planned international finance centre in St Helier are costing the island money, the treasury minister says.