David Cameron's election strategist owns and runs an offshore company in Malta, it has been claimed. The link between Lynton Crosby and the tax haven could make uncomfortable reading for the prime minister, who has described legal ploys to avoid tax as morally wrong.

The Daily Mirror reported that Crosby's Maltese firm, Rutland Ltd, was run from the offices of a trust firm specialising in "wealth preservation".

A spokesman for Crosby's UK firm, CTF Partners, confirmed that Crosby, an Australian who lives in the UK, was a non-domicile – "non-dom" – but insisted he paid his "full tax obligations".

After disclosures about the comedian Jimmy Carr using a legal scheme to avoid tax, Cameron said last year: "Some of these schemes we have seen are quite frankly morally wrong.

"It is not fair on hardworking people who do the right thing and pay their taxes to see these sorts of scams."

CTF is reportedly being paid £200,000 a year for working one day a week on plans to get the Tories elected in 2015.

The firm, which Crosby runs with fellow Australian Mark Textor and British director Mark Fullbrook, has offices in London, Sydney and Milan.

All three men are also shareholders in Rutland, set up in Malta in 2011 to provide "consultancy and technical services". The Mirror said there was no suggestion that Crosby or Rutland had broken the law.

Tax campaigners have questioned whether it was right for Cameron and the Tories to employ someone involved in a company based in a tax haven.

Crosby has been credited with sharpening the Tories' message and his interventions have been particularly welcomed by those on the right of the party. The Financial Times reported that last month he told 180 of the party's MPs that the key to success in the 2015 general election was to get its immigration message right.

A spokesman for CTF said Crosby paid tax in the UK on all his UK earnings at exactlythe same rate as any UK citizen. "It is categorically wrong and seriously damaging to claim Rutland is 'hiding the true identity of the company owners' as this has been a matter of public record for years.

"Rutland is a legitimate company, which fulfils all its tax obligations in Malta. It has never done any business in the UK or paid any dividends to anyone in the UK.

"It has not received fees from any UK company, body, or individual. Any claim, or attempt to claim, that it was set up, or is used, to avoid paying UK tax is categorically wrong and highly damaging."

A spokesman for the Conservative party referred queries to CTF Partners.