Ed Miliband said the non-dom rules were "indefensible" and axing them would raise "hundreds of millions" in tax.
But shadow chancellor Ed Balls was forced to deny contradicting himself after saying in January that scrapping the rule "would cost Britain money".
Chancellor George Osborne said Labour's plan had "unravelled".
The BBC's assistant political editor Norman Smith said the comments, in a BBC interview ahead of the election campaign, appeared to contradict what he and his leader were saying now about the party's most significant announcement of the campaign so far.
Mr Osborne said they were an example of the "economic confusion" that would result from a Labour government.
In other election news:
Non-doms are defined as British residents who pay tax on their UK earnings but whose permanent home is deemed to be outside the UK and therefore do not have to pay UK tax on foreign income as long as they do not transfer it to the UK - instead they pay a charge of at least £30,000 once they have been in the UK for seven years.
High-profile examples reportedly include Chelsea owner Roman Abramovich and HSBC chief executive Stuart Gulliver.
Former Conservative deputy chairman Lord Ashcroft gave up the status in 2010 to keep his place in the House of Lords after a change in the law barring non-doms from sitting in Parliament while architect Lord Foster quit the Lords at the same time.
Some Labour supporters including businessman Sir Gulam Noon also had non-dom status in the past.
Whose side are you on? It is one of the most powerful questions in politics and Ed Miliband believes it is the key to seeing him installed in Downing Street.
That's why Labour is targeting the so-called non-doms today. They're very rich, often foreign and enjoy a lifestyle that makes them resented by anyone who's struggled to make ends meet in recent years.
That is, incidentally, the same reason George Osborne targeted them to pay more when he was in opposition and increased the annual tax charge some pay in his last Budget.
Let's be clear though, these people are not tax dodgers. They pay tax on their UK earnings plus an annual charge of £30,000 or more to have a totally legal tax status that Gordon Brown as well as George Osborne decided to keep as they were advised they risked losing more in tax by scrapping it than keeping it.
Read Nick's full blog
Robert Peston: Are non-doms bad for the UK?
In his Autumn Statement in December, Chancellor George Osborne announced a new £90,000 charge for people who are non-domiciled in the UK for tax purposes but have lived there for 17 of the past 20 years.
The previous Labour government introduced a £30,000 charge for people resident in the UK for seven of the previous 10 years but who were non-domiciled for tax purposes.
Under Labour's proposals, no new people will be able to claim non-dom status after April 2016 while existing non-doms would have a "short period" to adjust their tax affairs.
Temporary exemptions of about two or three years would be available for students and foreign workers seconded to the UK for a short period of time, in consultation with business and universities.
This election issue includes income tax and national insurance levies and business taxes.
Policy guide: Where the parties stand
In a speech at the University of Warwick, Mr Miliband said non-dom status was an "arcane 200-year rule", allowing a "few people at the top" to "operate under different rules".
He said: "There are people who live here in Britain like you and me, work here in Britain like you and me, are permanently settled here in Britain, like you and me, were brought up here, but just aren't required to pay taxes like you and me."
What is non-domicile status?
Q&A: What is a non-dom?
Mr Miliband said he did not blame non-doms who were only "playing by the rules" but he insisted: "It isn't fair, it isn't just and it holds Britain back and we will stop it. The next Labour government will abolish the non-dom rule."
In a series of media interviews on Wednesday, Mr Balls endorsed the proposed changes, saying the clampdown could raise at least "hundreds of millions of pounds" and rejected claims it would lead to an exodus of businessmen.
"When we introduced tougher rules in 2008, people said people would leave the country," he told Radio 4's Today programme. "That isn't what has happened."
In a BBC interview in January, Mr Balls said he would be "tougher" on non-doms but appeared to cast doubt on axing their tax status as a whole.
He told BBC Radio Leeds: "If you abolish the whole status, then probably it ends up costing Britain money because there will be some people who then leave the country."
Asked on Wednesday afternoon about his earlier comment, Mr Balls said he had been speaking about the need to find a solution in relation to short-term visitors to the UK.
He accused the Conservatives of "throwing up a smokescreen" around Labour's policy to hide the fact it would "keep these unfair rules".
Labour said that in January, it was considering whether genuine temporary residents should be allowed any future leeway and that Mr Balls' comments then were in no way "inconsistent" with what it was now proposing.
Mr Osborne said: "Labour's policy is a total shambles... You have Ed Balls admitting it will cost Britain money and then when you look at the small print it turns out the majority of non-doms won't be affected so the headlines are misleading."
The Conservatives said they had taken the "right approach" in increasing the annual levy on non-doms and would continue to tackle abuse of the existing rules through a £5bn crackdown on tax evasion and avoidance.
The Liberal Democrats have also pledged to increase non-dom charges and reform eligibility criteria, saying this could raise an extra £130m.
Leader Nick Clegg said "the wheels are coming off" Labour's announcement and "in pursuing a headline they forgot that we must remain an open economy but of course not an economy that is open to abuse".
The Green Party said the changes "could not come a moment too soon" while UKIP said aspects of the non-dom rules were "ludicrous" but any reform must be thought through to ensure it didn't disadvantage the public finances.
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Labour has defended its plans to end the non-domicile rule that allows some wealthy UK residents to limit the tax paid on earnings outside the country.