Postal workers in west Lancashire will not be made to deliver free promotional copies of The Sun, the Royal Mail said.
The paper has agreed not to distribute the issues in Liverpool because of the continued anger at the way it reported the 1989 Hillsborough stadium tragedy.
It is understood six members of staff in Skelmersdale were at Hillsborough on the day of the disaster.
Postal workers said they were "pleased" after Royal Mail said refusals would be considered on a case by case basis.
The Sun has started a nationwide giveaway of more than 20m copies of a special free mini-issue across England ending on Friday, with the exception of Merseyside, to tie in with the start of the World Cup.
Postal workers said they would walk out if they were made to deliver the paper, when they discovered copies would be delivered in the WN8 postcode area.
After their concerns were raised to Royal Mail, it said it would consider actions by workers on a case by case basis.
A Royal Mail statement said: "If there are any personal reasons why a postman or woman would not want to deliver the mailing, we would consider these on an case by case basis working closely with the Communications Workers Union."
Following the decision, a statement was released on behalf of the postal workers in Skelmersdale, which said: "We are pleased to report that Skelmersdale and the rest of the WN8 area will not be receiving copies of The Sun through their letter boxes this week.
"We would like to thank the people of Skelmersdale and Liverpool for their support."
There has been a sustained campaign to boycott the newspaper in Merseyside since it published an article four days after the disaster, headlined "The Truth", which made allegations about fans' behaviour at Hillsborough.
The Sun published a full page apology in 2004 and, in 2011, James Murdoch, the then executive chairman of its parent company News International, issued a further apology on the paper's behalf.
Speaking on The Media Show on Radio 4, Stephen Abell, managing editor of The Sun, said: "When concerns were raised through Royal Mail, we worked out a way of dealing with it and that really has been our attitude to this."
The Communication Workers Union said it was not an official dispute but it had been seeking mediation with management.
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