An ambitious project to create a world-class arts complex in ­Scotland remains on budget, its organisers insist, after it was awarded £9.4m in lottery funding.

The V&A Museum is currently being built on the redeveloped waterfront in Dundee, and is due to be completed by 2016 and open in 2017.

Yesterday, the scheme received the bumper award from the ­Heritage Lottery Fund, but the announcement comes in a week in which concern has been raised that decisions over its future ­funding are being taken behind closed doors.

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The financial boost for the project, which will showcase displays from the V&A in London as well as Scotland's design heritage, comes after Dundee councillors pledged, in a private meeting, to support the project with £350,000 in revenue and £150,000 "in kind" for each of the 10 years from 2016/17.

Tenders to build the striking Kengo Kuma-designed building have now gone out to constructors within what organisers insist is a strict budget of £45m.

Funding support is also expected from the Scottish Government, which has already committed £15m to the capital budget, and Scottish Enterprise.

The V&A in London is not contributing money but has given its brand to the development, which a spokeswoman said was "priceless", as well as access to its huge collections for the scheme.

Philip Long, director of the V&A at Dundee, said the award was a "massive vote of ­confidence" in the project and said the HLF had scrutinised the bid "from top to bottom".

He said: "Scotland's achievement in design is world-class and centuries old. The development of V&A at Dundee will for the first time provide Scotland with a dedicated centre to celebrate that achievement, as well as a place to see and understand the design creativity of other cultures."

It was reported this week that securing funding from the council was linked to landing the Lottery funds. But yesterday a spokesman for the council declined to comment on the budget meeting.

Dame Seona Reid, the former head of Glasgow School of Art, and now deputy chairwoman of the Heritage Lottery Fund, said: "Today's decision brings HLF's investment in Scottish museums and art galleries to over £177mn.

"This new world-class museum is an exciting addition to the sector, providing a source of education and delight for visitors, while making a transformational contribution to the cultural, social and economic regeneration of the city."

The funding was also welcomed by Culture Secretary Fiona Hyslop and Scottish Secretary Alistair Carmichael.

Creative Scotland is currently considering a funding submission from the project. The organisers of the project are also seeking a further £15m from private sources, with £6.7m already raised.

The Scottish Design Galleries within the V&A will tell the story of Scotland's contribution to global design, with exhibits ranging from the 17th century to the modern day.

Earlier this week, a Dundee Labour councillor, Richard McCready said the council should have discussed the funding in public.

He said: "I was not elected to Dundee City Council to take ­decisions in secret."

The organisers of the V&A in Dundee are Design Dundee Ltd, a partnership between the Victoria and Albert Museum in London, Dundee City Council, the University of Dundee, the University of Abertay and ­Scottish Enterprise.

The content of the displays in the galleries is currently still being developed, but will include designers, engineers and artists such as Phoebe Anna Traquair, Charles Rennie Mackintosh, ­Edinburgh Weavers, Sir Basil Spence, Holly Fulton and ­Alexander McQueen.