Cities that fail to adopt the idea of electing their own US-style mayors will lose out on jobs and investment to UK and overseas rivals, David Cameron said.
In an appeal to voters in 10 English areas holding referendums on May 3, he warned that they needed to "join the race or fall behind" in attracting cash.
Having a single high-profile figure at the helm of major urban areas would also help close the "yawning gap" between parts of the north and London and the south east, he suggested.
Votes are due to be held next month in Bristol, where the premier was addressing pro-mayor activists, along with Bradford, Leeds, Manchester, Newcastle, Nottingham, Sheffield, Wakefield, Coventry and Birmingham.
Mr Cameron said they were all "in an out-and-out race for jobs, wealth and investment" with rivals across the globe as the West seeks to recover from the financial meltdown.
"Bristol isn't just competing with London - it's competing with Bangalore, Beijing, Berlin. And in this race our cities have got to have more of an international presence," he said.
He said he wanted mayors to follow his lead of travelling the globe to seek out contracts, pointing to £100 million attracted to the capital by Tory mayor Boris Johnson.
"Whenever I go on a major trip abroad I load up a plane with business people so we can bang the drum for trade. I want a whole load of powerful British mayors with the same attitude pressing their business cards into the hands of those who can bring wealth and work back home."
He went on: "If the CEO of some big Japanese manufacturer or Gulf investment fund wants to call Bristol or Leeds or Bradford, they need to know who to call.
"They don't want to speak to an anonymous official, they want to talk to the person with clout, who holds the purse strings, calls the shots and runs the city. And that person is the mayor.
"This has got to be part of a bigger drive for Britain to get out there and sell to the world more aggressively."
Promoting the election of mayors as a weapon to combat the north-south divide, he said: "There's been a yawning gap between north and south.
"Frankly nothing we do in Westminster - no policy we pass or investment we make - can compete with having one energetic champion on the ground, whose round-the-clock, unrelenting focus is on seeing their city succeed.
"So our dream is to have real heavyweight, influential figures in the north, the Midlands and the west, ones who can give their city a distinctive identity, who can fight their corner and who will help rebalance our country."
Mr Cameron said having a single figure at the head of each city was also a form of "undiluted democracy" that would greatly improve accountability
"Let's be clear what this moment means. It's not some trivial restructure or fiddling about - it's about more investment across our country, more jobs for our workers, more life in our political system.
"It's a once-in-a-generation chance to change the way our country is run.
"I passionately want those cities - from right here in Bristol to Birmingham, Nottingham to Newcastle, Sheffield to Wakefield, to give a resounding, emphatic 'yes' next week.
Mr Cameron's speech came on St George's Day, and Labour used the occasion to press for greater devolution within England and a revival in national pride.
Shadow communities secretary Hilary Benn said that despite the widespread extra freedoms given to Scotland and Wales, most decisions affecting English regions were still taken in London.
The debate over Scottish independence would only increase the gap, he wrote on the Daily Telegraph website, calling for "a radical devolution of power to local communities".
"After all the population of Yorkshire and Humberside is bigger than Scotland, and the north of England economy is more than twice the size of the Scottish economy," he said.
"All of these will need local leadership with Government giving communities the tools, powers and finance they require to do the job."
He went on: "It is how our great English cities grew in the 19th century when local government brought homes, schools, hospitals, gas, electricity and clean water that transformed lives.
"And the challenges of our age are just as great.
"That's why we should say to local communities and local government in England - cities and counties - that we are prepared to devolve power over transport, infrastructure, skills, and economic development, and that we will devolve these things in the way that you want it."
Mr Benn said he also wanted to "reclaim the flag of St George" from far-right groups as part of a renewed celebration of Englishness.
"While we are proud to talk about being English when it comes to sport, in politics there has been some reluctance to talk about Englishness in the way that our friends and relatives in Scotland, Wales and Northern Ireland celebrate their national identity. We should change that and talk proudly about being English.
"And we should reclaim the flag of St George from those whose values certainly do not represent what our nation is all about. Our flags - the Union Jack and the Cross of St George - belong to all of us."