The Pope was unable to travel to Oceania
The 81-year-old pontiff transmitted the message, his first"virtual" apology, in a recent string of statements of contrition, from a laptop in the Vatican's frescoed Clementine Hall on Wednesday.
"The Church expresses deep regret and asks forgiveness where her children have been or still are party to these wrongs," the document said.
The report singled out the "stolen generation" of at least 30,000 Aboriginal children in Australia who were forcibly separated from their parents in a church-backed government attempt to educate them and assimilate them into white culture.
The leader of Australia's opposition Labor Party appealed on Friday to the government to make a formal apology to the nation's indigenous people.
Simon Crean, who was elected Labor leader on Thursday, said lasting reconciliation could not come about without saying "sorry" and initiating dialogue.
Prime Minister John Howard has refused to apologise, arguing modern Australians should not say sorry for actions they did not personally commit.
Sexual abuse
His message also addressed the issue of sexual abuse: "In certain parts of Oceania, sexual abuse by some clergy... has caused great suffering and spiritual harm to the victims," the document acknowledged.
The Pope gave no details of the cases he was referring to, but internal Vatican reports documenting instances where priests and missionaries had forced nuns to have sex with them - and even to have abortions afterwards - have come to light in recent years.
"Sexual abuse within the Church is a profound contradiction of the teaching and witness of Jesus Christ.
"The synod fathers wished to apologise unreservedly to the victims for the pain and disillusionment caused to them," the pontiff wrote.
Jews and Orthodox
This is just the latest in a series of papal apologies for the sins of the Roman Catholic church.
Last month, Pope John Paul II apologised to China for the errors of missionaries in colonial times.
On controversial visits to both the Ukraine and Greece earlier this year, he asked Orthodox Christians' forgiveness for wrongs committed against them by Roman Catholics.
And in a trip to Israel last year, he publicly asked God's forgiveness for the sins of Roman Catholics through the ages, including wrongs inflicted on Jews, women and minorities.
However, the Pope stopped short of travelling to the other side of the world to deliver this message in person.
"I would have wished to visit Oceania once again," he said, "but it was not to be."