The ongoing saga of Zaha Hadid Architects (ZHA) and the Tokyo 2020 Olympic stadium job took a new twist last night when ZHA and partner Nikken Sekkei issued a statement saying they were throwing in the towel, citing an inability to secure a construction partner. Getting the stadium built for an acceptable price has been at the heart of the difficulties.

ZHA originally won the contract to design the stadium in November 2012, ahead of other bidders such as Populous, UNStudio and Toyo Ito. They beat Cox Architecture into second place and SANAA into third.

But the bid was always controversial, and this summer, in series of astonishing events, ZHA was given formal approval on 7 July, only for the scheme to be cancelled by Japanese prime minister, Shinzo Abe, just 10 days later.

In announcing the cancellation, he said the cost of the $2bn stadium “has just ballooned too much”. The design had also suffered stinging criticism from a number of leading Japanese architects.

A succession of skirmishes followed, with ZHA issuing a robust defence of their design, blaming the huge cost increases on Japan's overheated construction market and the tendering process for the building, in which contractors were appointed before they submitted cost estimates: "Our warning was not heeded that selecting contractors too early in a heated construction market and without sufficient competition would lead to an overly high estimate of the cost of construction,” they said.

Sir Richard Rogers, who was on the jury that first selected the design, came out publicly in support of ZHA, saying: "I'd like to express my concern about the decision to cancel Zaha Hadid Architects' design at this late stage.

"For Japan to lose their nerve now, and abandon a design by one of the world's foremost living architects that was selected by an international jury, will not only result in a poorer quality stadium for the Tokyo 2020 Olympics, but also in damage to Japan's international credibility, and reputation as a promoter of world-class architectural design."

ZHA were not going to go quietly, so when Japan announced a new design and build competition for the job on 1 September, they announced they would re-bid, working with Nikken Sekkei. “We believe the best way to respond to the new brief is to maximise the use of the expertise and experience gained by the design team over the past two years,” the firm stated.

The revised guidelines for the new competition capped the cost at ¥155 billion (£850 million) – a significant reduction compared to the ¥250 billion (£1.37 billion) estimate for ZHA's initial design. The amount of seating has also been reduced.

The new competition requires bidders to demonstrate capabilities in planning and design, construction and construction supervision, and to form consortiums of firms to cover all these capabilities and in last night's statement, Nikken Sekkei and ZHA said they had not been able to secure a construction company in their consortium and that "as a result they are unable to enter the competition.”

ZHA said: "It is disappointing that the two years of work and investment in the existing design for a new National Stadium for Japan cannot be further developed to meet the new brief through the new design competition.

"Nikken Sekkei and ZHA are prepared and able to deliver a cost-effective stadium that meets the revised brief, is ready in good time for the 2020 Games and provides a new home for sport in Japan for generations to come," they said.

There is one last opportunity for ZHA to maintain an involvement with the project – the practice says it hopes to lend the knowledge it has gained during the project to whoever eventually wins the competition: "While the current competition is closed to the existing design team, we stand ready to use the wealth of detailed knowledge and expertise, built up through the thousands of hours dedicated to the project, to assist the National and Tokyo Governments and Japanese people deliver a stadium fit to welcome the world in 2020 and go on to host national, international and community events for the next 50-100 years," said the statement.

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