People could then choose between an independent Wales at Europe's "heart" or a "forgotten second-class region in a dying British state," he said.
The independence call goes further than his party conference speech in March.
Polling for BBC Wales has put support for independence at less than 10% since 2011.
Mr Price said Wales should hold a "new national conversation" about the country's future whatever happens with the UK's departure from the European Union.
In last month's speech to party members, in Bangor, he called for an independence referendum if a series of post-Brexit demands were not met.
His demands included a call for European funding for Wales to be guaranteed, cuts in VAT for tourism and construction, the devolution of powers over air passenger duty, and control over migration policy.
But now Mr Price has gone further by making a Welsh independence referendum dependent on whether Brexit goes ahead without a second EU referendum.
In last month's speech to party members, in Bangor, he called for an independence referendum if a series of post-Brexit demands were not met.
His demands included a call for European funding for Wales to be guaranteed, cuts in VAT for tourism and construction, the devolution of powers over air passenger duty, and control over migration policy.
But now Mr Price has gone further by making a Welsh independence referendum dependent on whether Brexit goes ahead without a second EU referendum.
"It is broken Westminster, not the EU, which has failed the people of Wales," he said.
"I do not believe that the poverty facing our country is inevitable and nor will these problems be fixed by Brexit.
"They will be fixed by taking our future into our own hands and becoming a nation in our own right."
His comments follow a demand by the Scottish First Minister Nicola Sturgeon on Wednesday for a second referendum on Scottish independence by 2021 if Scotland is taken out of the EU.
Mr Price added: "Whatever happens with Brexit over the next few months we should begin a new national conversation about what kind of future we want for Wales by establishing a Welsh Citizen's Assembly along the lines proposed in Scotland."
Asked to choose between a range of options in terms of Welsh powers, only 7% of Welsh voters backed the idea of Welsh independence in the 2019 St David's Day poll for BBC Wales - support has been less than 10% since 2011.
He's only seven months into the top job but Adam Price has already been on a journey with his messaging around Welsh independence.
From it being "on the table" after Brexit in October, to demanding it should happen if certain post-Brexit tests aren't met in March. Now he's gone even further.
"This is part of the Price project - we're not shying away from it," a Plaid source tells me.
It's a remarkable change from Leanne Wood's leadership, when the independence issue was never really part of Plaid's retail offer.
There have been concerns that placing the 'I' word front-and-centre would scare away potential voters, particularly in Labour heartlands.
Brexit has changed that thought process. In a period of political upheaval with people asking questions about our place in the EU and the future of the UK, Plaid Cymru's top brass think it is legitimate to raise the prospect of Welsh independence.
It's a bit of gamble a couple of years away from the next assembly election in 2021 - one the party hopes will pay off but, with independence seemingly still a minority pursuit, it could turn out to be a bit of a flop.
There are eight parties fighting for four MEPs in the planned European elections in May.
Welsh Labour, the Welsh Conservatives, Plaid Cymru, the Welsh Liberal Democrats, UKIP and the Green Party are joined by new groupings Change UK and the Brexit Party.