News Corp Chairman and CEO Murdoch apologised for an 'anti-semitic' Tweet (Reuters)

Rupert Murdoch has apologised for a tweet in which he criticised the "Jewish-owned press" for its coverage of the Israeli-Gaza crisis.

The media mogul tweeted "unreservedly" his apologies and wrote to the the Anti-Defamation League (ADL), which called his remarks "awkward and inappropriate", to say sorry.

Murdoch, a long-time backer of Israel, had accused some media outlets of being overly critical of Israel's handling of the crisis in Gaza.

"Why Is Jewish-owned press so consistently anti-Israel in every crisis?" the News Corp chairman and chief executive tweeted.

Earlier he had accused CNN and AP - which are not "Jewish-owned" - of being "biased to the point of embarrassment".

Although pro-Israel, the tweet's reference to a Jewish-owned press "could play into the age-old anti-Semitic conspiracy theory about 'Jewish control' of the news media," said ADL director Abraham Foxman.

"Jewish-owned press has been sternly criticised, suggesting link to Jewish reporters," he tweeted in response to the criticism. "Don't see this, but apologise unreservedly."

In his letter to ADL he said: "I feel very strongly about the righteousness of Israeli's cause, particularly when its citizens are under missile attack. So I do get very upset when I see coverage that I feel is unfair and biased towards Israel.

"But I should have stuck to the substance of the issue and not [brought] in irrelevant and incorrect ethnic matters."