The Superfast Cymru contract was set up to connect 96% of businesses and homes excluded from commercial roll-out and the project has so far reached 581,000 premises across Wales.
Concerns have been raised about the deadline being met, although Superfast Cymru said it was "on track".
The Welsh Government has part-funded the project, investing £205m into the initiative but industry experts thinkbroadband.com said they do not believe the deadline can be met.
Andrew Ferguson, editor of thinkbroadband.com, said: "We don't believe 96% can be hit this month at all. Current rates suggest the end of 2016.”
He said the scheme had a "confused history" with "targets all too often misrepresented" and according to thinkbroadband.com, the cost of the project is £430 per customer.
It said 88% of Wales was now covered by superfast broadband speeds of 24 Mbps or more - less than England's 90.7% coverage, but more than Scotland's 85.3% and Northern Ireland's 80.1%.
The latest Welsh Government figures from March showed only 57% of eligible customers in Powys are connected.
In a joint statement, BT and Welsh Government said: "The original Superfast Cymru contract target is anticipated to be completed by BT by end of June 2016, followed by robust Welsh Government testing and verification taking it to summer 2016.
"We are currently exploring the geographical and technical aspects of extending coverage of superfast broadband to the final few premises in Wales.
"This means that every premises in Wales has the ability to request faster broadband, helping make sure that no communities are left behind."
They added they were "still confident" that 40% of premises will eventually have access to speeds of 100 Mbps through a combination of FTTP (fibre to the premises) and FOD (fibre on demand) technology.