The £13bn Wylfa Newydd nuclear power project delay "is not a stop", a Hitachi spokesman has told the BBC.
Director of Corporate Affairs Leon Flexman said the project was costing £1m a day which could not continue "forever".
Welsh Secretary Alun Cairns said he was "confident" the plant would still be built on the Anglesey site but would be delayed for a "small number of years".
Mr Flexman said financing was "the final piece of the jigsaw".
"Hitachi never said it would finance the entire construction phase," he told BBC Radio Wales' Good Morning Wales programme.
"It is not a stop, we are halting the activities until it can be restarted providing the right conditions are in place and the finance is there."
But he added he could not say what would happen if an agreement is not reached on funding.
"I can't comment on the future when we don't know if those conditions will be met."
Mr Flexman said: "Wylfa Newydd is the best site probably in Europe for nuclear new build... but we have to be realistic that efforts to progress the project cant continue at the pace they are now.
"The reason for the postponement is it is a huge ask for any private sector company to bear all the financial burden of a nuclear power station... it requires participation from governments as well but the terms on which you do that... is a very complicated business.
"When you're spending a million a day, you just can't keep doing that forever as a responsible private company."
He added there was a possible solution and the conversation "needs to continue because the benefits the project can bring are worth the extra efforts", and said the apprenticeship schemes put in place by Hitachi, the parent company which owns Horizon Nuclear, would be honoured.
Economy Secretary Ken Skates said it was "hugely important that the momentum of the work can be maintained".
Mr Cairns said he was confident for the future of Wylfa after Business and Energy Secretary Greg Clarke said the UK government was willing to consider taking a one-third equity stake in Wylfa.
He said this showed the UK government's commitment to the project.
Mr Cairns said the project could still happen "without a question" and he was optimistic Hitachi would find a partner or partners to share the cost.
Peter Hughes, Unite union regional secretary for Wales, fears a delay of a few years could "turn into a decade".
He added: "It's a major disappointment. It won't be until they put a shovel in the ground, we'll actually know whether its going to be built.
"It's disappointing for young people looking forward to actually starting [work] at Wylfa. When you're looking for a long term future there's not really big manufacturing or a big infrastructure in place for these young people to work on."
By Sarah Dickins, BBC Wales economics correspondent
While the shock that the massive Wylfa Newydd project is being suspended resonates across Anglesey and north Wales, there is already talk about what next.
It's important to remember Hitachi still owns the land and it has invested £2bn here. Not surprisingly it has kept the door open in terms of perhaps developing nuclear energy on Anglesey in the future.
It is significant that Hitachi says it will continue to discuss a nuclear programme with the UK government.
The reason for abandoning the project at this point was financial. Investors were not finding it attractive enough.
The nuclear sector, at the moment, is one where vast amounts of money are needed up front and investors only get paid once electricity is being generated.
That's in sharp contrast to, for instance, Heathrow Terminal 5 or the massive Thames sewer project. In both of their cases investors are paid during the construction phase.
In terms of individuals who have been trained for jobs as part of the Wylfa Newydd project, they will still have those skills they have gleaned.
The challenge is for those in authority to try to attract other investment and projects that can use those skills.
Those in renewable sectors; on and off-shore wind, solar and marine, may argue that investing so much time, energy and money in one large project was unwise. They will argue governments should now encourage more smaller renewable schemes across Wales.
About 9,000 workers had been expected to build the Anglesey plant by mid-2020 and business leaders have called the delay "a tremendous blow".
Energy is not currently devolved to the Welsh Government, but Mr Skates has said an emergency economic ambitions board meeting will take place on Monday and that he was "in close dialogue with Horizon Nuclear Power".
Mr Skates said Mr Clarke's statement was welcome but left "a number of very significant questions for the island of Anglesey, north Wales and Wales as a whole".
He said: "Together, we will continue to put pressure on the UK government to move things forward."