India's Tata Steel plans to sell its loss-making UK business, putting the jobs of thousands of workers at risk.
Its European holding company has been told to "explore all options for restructuring", including the partial or entire sale of its UK operations.
Union leaders travelled to Mumbai in a bid to persuade Tata to keep making steel at plants including Port Talbot.
The UK and Welsh governments said they were working "tirelessly" to ensure the future of the British steel industry.
Meanwhile, Plaid Cymru leader Leanne Wood said that her party wanted the Welsh Assembly to be recalled to discuss the crisis - a call that was echoed by Welsh Conservatives leader Andrew Davies.
Tata's restructuring decision, which was announced after a board meeting in Mumbai on Tuesday, will also affect workers at its other UK plants including Rotherham, Corby and Shotton.
Tata said trading conditions had "rapidly deteriorated" in the UK and Europe due to a global oversupply of steel, imports into Europe, high costs and currency volatility.
"These factors are likely to continue into the future and have significantly impacted the long-term competitive position of the UK operation," it said.
That means finding a buyer for the whole business may not be easy.
Colin Hamilton, commodities expert at Macquarie Group, told the BBC: "Steel demand is still falling. It peaked in 2013. It is very hard to see who would buy the 'hot end' of the business, the steel making end itself, although the rolling mills are more attractive, I think its is unlikely we will see a buyer for the business as a whole."
In a joint statement, the UK and Welsh governments said: "We remain committed to working with Tata and the unions on a long-term sustainable future for British steel-making.
"Both the UK and Welsh governments are working tirelessly to look at all viable options to keep a strong British steel industry at the heart of our manufacturing base."
Labour MP Stephen Kinnock, whose Aberavon constituency includes the Port Talbot plant, accompanied the union delegation to Mumbai.
He said: "The fact that Tata Steel is committed to continuing and to moving forward with the plant whilst looking for a buyer... is absolutely critical.
"There were various scenarios before we came out here... We are now a little bit clearer on which scenario we now have and it isn't certainly the worst case scenario."
Labour leader Jeremy Corbyn said: "Ministers must act now to protect the steel industry and the core of manufacturing in Britain."
Unions expressed concern at the announcement and urged Tata and politicians to work at finding a buyer for the business.
Roy Rickhuss, general secretary of steelworkers' union Community, said the "worst fear" that Tata would announce plant closures had not been realised.
It was, he added, "vitally important" the company acted as a "responsible seller of its businesses and provides sufficient time to find new ownership".
He said: "There is also a crucial role for both the Welsh and UK governments to do all they can to ensure a future for Tata's remaining UK steel businesses and to provide every assistance to secure a buyer that will continue steel making."
Len McCluskey, general secretary of the Unite union, described Tata's decision as a "very dark day for the proud communities and a proud industry which is now on the verge of extinction in this country".
Dave Hulse, national officer of the GMB union, said the news was "absolutely devastating", adding: "Tata has let the whole of the UK steel industry down."
Tata Steel has been operating in the UK since 2007 when it bought Anglo-Dutch steelmaker Corus.
In January the company announced more than 1,000 UK job cuts, including 750 in Port Talbot, where it employs 4,000 staff and a further 3,000 contractors and temporary workers.
And last October Tata Steel said nearly 1,200 jobs would go at plants in Scunthorpe and Lanarkshire.
There have been allegations that Chinese steel is being "dumped" on world markets at prices that UK plants cannot hope to compete with.
At the same time China's economy has remained sluggish, meaning that its need to export has grown as the demand for steel from its construction sector weakens.
Other factors affecting the wider UK steel industry include relatively high energy prices and the extra cost of climate change policies.