Oscar-winning actor Geoffrey Rush is suing News Corp's Sydney masthead The Daily Telegraph over a series of allegations the publication has run in the past week.

Speaking at a press conference in Melbourne, the Pirates of the Caribbean star described claims made by the publication as "slurs" and "hyperbole".

"The Daily Telegraph has made false, pejorative and demeaning claims, splattering them with unrelenting bombasity on its front pages," he said.

"This has created irreparable damage to my reputation [and] been extremely hurtful to my wife, my daughter and my son. The situation is intolerable and I must now seek vindication of my good name through the courts."