* Minister says taxes won't rise for top earners
* Comment contrasts with tax plans of opposition Labour Party
* Opinion poll lead of May's Conservatives narrowing
* Election due on June 8, followed by first Brexit talks (Adds comment from PM May)
LONDON, June 3 (Reuters) - An ally of British Prime Minister Theresa May has said income tax will not rise for higher earners in an apparent new promise to voters less than a week before a national election with opinion polls showing a narrowing of her lead.
The comments from Defence Minister Michael Fallon to a newspaper, which May sought to play down, looked like the latest mixed message from the ruling Conservatives who have seen their popular support fall ahead of the June 8 election.
Polls suggest the Conservatives are set to win but are no longer likely to get the kind of landslide victory that would have boosted May ahead of the launch of complicated negotiations on Britain's exit from the European Union.
Fallon told the Daily Telegraph that the Conservative Party would not hike the top rate of income tax, striking a contrast with the main opposition Labour Party.
The Telegraph said it asked Fallon if high earners could be sure their taxes would not go up under a new Conservative government, to which he replied: "Yes. You've seen our record. We're not in the business of punishing people for getting on. On the contrary we want people to keep more of their earnings."
"The only way they can be sure their taxes won't rise is to vote Conservative," he said.
But May, asked by reporters whether Fallon's comments meant the Conservatives were shifting their position on tax, said there had been no change.
"We've set it out in the manifesto. What people will know when they go to vote on Thursday is that it is the Conservative Party that always has been and is and always will be a low-tax party," she said during a campaign stop.
May called the snap election in April when opinion polls were showing she had a lead of more than 20 points over Labour under the leadership of left-winger Jeremy Corbyn.
But since then May's lead has been eaten away, meaning she might no longer score the thumping victory she had hoped for ahead of this month's launch of Brexit negotiations.
A poll showed on Friday that the Conservatives were ahead of Labour by five percentage points, down sharply from 15 a little more than two weeks earlier. Another poll this week said the lead was down to three points.
The decline in support for the Conservatives coincided with a surprise announcement by May last month that she would make elderly people pay more for their social care, despite concerns that it could undermine support among aging, wealthy homeowners - a core source of Conservative vote.
May later softened the proposal by saying there would be a limit on the amount that people would have to pay.
The latest confusion over income tax underscores the challenge facing the next government to meet the growing costs of public services at a time when Britain's budget deficit remains large, and with Brexit-related uncertainty likely to weigh on the economy.
When May unveiled her election policies last month, she left open the possibility of higher income taxes by only promising no rises in value-added tax and dropping a Conservative pledge under predecessor David Cameron - made in the 2015 election campaign - not to raise income tax, national insurance contributions or VAT.
The constraints of that pledge became clear earlier this year when May's government tried to increase national insurance contributions on self-employed workers. It was then forced into a U-turn after Conservative lawmakers, wary of alienating small businesspeople, protested that it broke the 2015 pledge.
On Saturday, Labour said Fallon's comments showed the Conservatives were protecting higher earners at the expense of the less well-off.
"The mask has finally slipped," John McDonnell, a lawmaker who would be finance minister if Labour win the election, said in a statement. "The only guarantee the Tories are prepared to give at this election is to big business and high earners."
Labour has said it will raise income taxes on people earning more than 80,000 pounds ($103,152) a year, while promising no increases for the other 95 percent of taxpayers.
($1 = 0.7756 pounds) (Writing by William Schomberg; Editing by Mark Heinrich)