Mr Brown was accused of misspelling a dead soldier's name
Prime Minister Gordon Brown has "the most enormous personal regard" for Sun newspaper owner Rupert Murdoch, Downing Street has said.
The Tory-supporting paper has been highly critical of Mr Brown over the equipment to troops in Afghanistan and a letter he wrote to a bereaved mother.
It has been reported that Mr Brown telephoned Mr Murdoch to complain but a spokesman did not confirm or deny this.
Business Secretary Lord Mandelson has called the Sun's reporting "crude".
The newspaper is critical of the standard of equipment provided for troops in Afghanistan.
It has also attacked Mr Brown over a letter of condolence he wrote to bereaved mother Jacqui Janes after her son Jamie was killed in Helmand, Afghanistan.
It says he misspelt her surname as "James" and overwrote a mistake he made writing the name Jamie - rather than starting the letter again.
The prime minister - who has poor eyesight - later apologised for "any unintended mistake".
Asked whether Mr Brown had called Mr Murdoch to complain about the Sun's coverage, a spokesman said the prime minister had regular contact with the media mogul.
But he refused to divulge the content of their conversations.
On Wednesday Lord Mandelson accused the Sun of portraying the government as the "enemy" of UK troops in Afghanistan rather than the Taliban.
The paper's criticism of the prime minister's letter to Mrs Janes amounted to "crude politicking" in favour of the Conservatives, he said.
But the Sun said it was "immensely proud" of its coverage of Afghanistan.
The newspaper, which had supported Labour since 1997, announced in September that it was switching allegiance to the Conservatives.