Welsh Conservative leader Andrew RT Davies said he was baffled by Mr Jones’ comments.
Speaking to BBC Wales’ Sunday Politics Wales programme, Mr Jones said: “At the moment there are rules. There are EU state aid rules that govern what we can and can’t do.
“If there are no rules, it becomes a free-for-all. That’s a bad thing for any single market.”
EU state aid rules regulate how much help governments can give to local industries.
Mr Jones said an inability to set UK-wide trade rules after Brexit “could cost jobs, it could cost a lot of money – that affects ordinary people, and that needs to be resolved as soon as possible.”
Welsh Conservative Leader Andrew RT Davies said: “I’m baffled by his pronunciation of a trade war.
“As I last looked at the constitutional settlement, trade and industry certainly wasn’t devolved and international negotiation was not devolved.”
Mr Jones also told the programme that the battle to keep the United Kingdom together “will be lost” unless the UK government starts listening to the devolved nations.
“We can share power in the UK, we can still be stable, we can still have the union, but the UK government needs to realise this now otherwise the battle will be lost,” he said. “They need to wake up and smell the coffee.”
Senior party figures from across Britain, including former prime minister Gordon Brown, will attend the launch of the constitutional convention in Cardiff at the end of March. The first minister first called for a UK-wide constitutional convention five years ago.
Plaid Cymru criticised the announcement, adding that Wales needed its own constitutional convention.
Adam Price, the party’s economy spokesman, said: “Rather than the Labour party talking to itself, why doesn’t it talk to the rest of us?”
UKIP assembly group leader Neil Hamilton said he thought Brexit would lead to “more powers” to the devolved institutions.
Welsh Liberal Democrat leader Mark Williams welcomed the convention but said “there’s a much bigger question than what we’re being presented with at the moment and that requires an UK response”.
Prime Minister Theresa May said disability y benefits should go to “really disabled people” not those “taking pills at home, who suffer from anxiety”. No 10 policy unit head George Freeman said personal independence payments (PIP) reforms were needed to roll back the “bizarre” decisions of tribunals.
Boris Johnson is due to hold talks with Egypt’s president on his first visit to the country as foreign secretary. Johnson says he will discuss a “wide range of issues and deepen the strength of our bilateral relationship” when he meets President Abdul Fattah al-Sisi and Foreign Minister Sameh Shoukry.
Theresa May has warned MPs not to “obstruct” the will of UK voters by changing the parliamentary bill aimed at getting Brexit talks under way. The Commons is beginning detailed scrutiny of the European Union Bill, with Labour, SNP and Lib Dem MPs seeking concessions.
Former chancellor George Osborne has warned a “deep constitutional crisis” would be caused if MPs vote against triggering Brexit. Mr Osborne said rejecting the government’s Article 50 bill could “pit Parliament against people”. He was speaking as MPs began a second day of debating the draft legislation that will allow formal talks to begin.
Jo Stevens has quit as Jeremy Corbyn’s shadow Welsh secretary after he forced Labour MPs to back the Article 50 bill. The Cardiff Central MP said she believed Brexit was “a terrible mistake” and said she “cannot reconcile my overwhelming view” that to endorse the bill would make it inevitable.
Sunday UK Foreign Secretary Boris Johnson arrived in the US for what his office said was a series of meetings with President-elect Donald Trump’s closest advisers and congressional leaders. Johnson, a former mayor of London, became the principle diplomat for one of the US’ strongest partners following the narrow success of 2016’s referendum to leave the European Union, commonly referred to as Brexit. Johnson was among the referendum’s highest profile supporters.
Theresa May said the UK cannot expect to hold on to “bits” of its membership after leaving the EU. The prime minister’s comment came after she was asked whether she would “prioritise” controlling immigration over staying in the single market.
Prime Minister Theresa May is planning to meet with President-elect Donald Trump in spring 2017 although no firm timing has been arranged, her office confirmed Thursday evening.