Secretary of State for Wales Alun Cairns is visiting Anglesey to 'reinforced his commitment' to deliver new nuclear in north Wales.
Hitachi announced it is suspending its involvement in the Wylfa Newydd project in its current form on Thursday.
The £20bn Wylfa Newydd has promised to be a new generation of nuclear power station in the UK with high paid skilled jobs.
Almost 400 jobs are now at risk.
Horizon, the company owned by Hitachi and who are in charge of developing UK power stations, said they have been in close discussions with the UK Government and had made "strong progress" but have been "unable to reach an agreement".
Work on the Oldbury project in Gloucestershire has also been suspended.
Mr Hawthorne, confirmed it will have a "significant impact" for those involved in the project and the company will begin consultation "immediately".
He said nuclar remained "critical to delivering the secure, low carbon and affordable energy the UK needs."
"Wylfa Newydd... remains the best site for nuclear development in the UK and we remain committed to keeping channels of communication open with the Government and our other key stakeholders regarding future options and both our sites."
First Minister Mark Drakeford and the Economy Minister Ken Skates said they will continue to press the UK Government to bring the project to Anglesey.
Ken Skates added he is seeking clarity on what the announcement of the suspension actually means.
"We need urgent assurance from UK Government about its intentions in respect of securing a funding model that will deliver major infrastructure projects like Wylfa Newydd.
“I will be in North Wales today, and will be on Anglesey to meet Ynys Mon Council and I will also be speaking again with Horizon and other local stakeholders. These discussions will continue with urgency over the coming days."
Alun Cairns said the UK Government will "continue to engage with Hitachi" and the site itself still has potential as an "attractive option for new nuclear projects."
The announcement does not spell the end for opportunities at Wylfa. All parties continue to see potential in the site and the UK Government stands ready to discuss options for Hitachi or other partners to deliver new nuclear in north Wales.
While unions have called for the UK Government to step in to make the project happen, environmental campaigners have called for a rethink of the UK's energy policy.
Sara Medi Jones, acting general secretary of the Campaign for Nuclear Disarmament (CND), said, the decision is "good news" because it "opens the door to investment in the renewable technologies of the future."
"Hitachi's decision proves once again that there isn't an economic case for new nuclear, certainly not when renewables like offshore wind are cheaper sources of energy."
Albert Owen, Labour MP for Ynys Môn told ITV News all governments and local authorities "must work together" to secure the future of the plant - otherwise the potential for 8,000 jobs will be lost.
Of the three new nuclear power stations planned, only Hinkley Point in Somerset has begun construction. Plans for a new nuclear station in Cumbria were scrapped in November.
With a reduction in fossil fuels, nuclear has been seen by the government as a key component in electricity generation in the decades ahead.
Shadow Business Secretary Rebecca Long Bailey MP described the government's nuclear strategy as a "full blown crisis."
Financial Times' Tokyo Bureau Chief Robin Harding told ITV News the UK Government will need to make a "real change of policy" to persuade Hitachi to reinstate work on the project.
A Business Department spokesman said: "As the Business Secretary set out in June, any deal needs to represent value for money and be the right one for UK consumers and taxpayers."
Despite extensive negotiations and hard work by all sides, the Government and Hitachi are unable to reach agreement to proceed at this stage. This Government is committed to the nuclear sector, giving the go-ahead to the first new nuclear power station in a generation at Hinkley Point C, investing £200 million through our recent sector, which includes millions for advanced nuclear technologies.
Hitachi have already spent over £800 million in preparation work of the site.
The original power station closed in 2015.