Vebjoern Selbekk, who initially defended his 10 January publication of the cartoons in Magazinet as an expression of press freedom, shook hands after his apology with a Muslim leader in Norway who said he considered the controversy over.
"I address myself personally to the Muslim community to say that I am sorry that your religious feelings have been hurt," Selbekk told a news conference on Friday.
"It was never our intent to hurt anyone.
"I, as editor, did not fully understand how hurtful the publication of the facsimile was. I would like to apologise for that today."
He also said he "deeply regretted" upsetting Muslims.
Selbekk, among the first to reprint cartoons which appeared last year in the Danish newspaper Jyllands-Posten, had first said he had no reason to apologise.
Protesters in Syria attacked the
Danish and Norwegian embassies
He says he has received more than 20 death threats by e-mail.
Thousands of Syrian demonstrators set fire to the Norwegian and Danish embassies at the weekend and Norwegian troops in Afghanistan have come under attack from protesters.
Norwegian flags have been burnt in Palestinian demonstrations.
Selbekk backed down partly last week, saying he would not have published the cartoons, including one of Prophet Muhammad wearing a bomb-shaped turban, if he had known the reactions they would provoke.
The Islamic Council in Norway welcomed Selbekk's apology and said they would protect him.
"Anyone who touches him, touches us," said Muhammad Hamdan, leader of the council who shook Selbekk's hand after a joint news conference hosted by Norway's Minister of Labour and Social Inclusion Bjarne Haakon Hanssen.
"Our Prophet Muhammad has said that everyone can make mistakes but the best is the one who expresses regret and asks for forgiveness"
Norway Islamic Council leader
"I understand ... that he has children the same age as mine. I want his children to grow up together, live together in peace, and become friends," Hamdan said.
"Our Prophet Muhammad has said that everyone can make mistakes but the best is the one who expresses regret and asks for forgiveness," he said.
Hanssen praised Selbekk and Hamdan for their accord.
"When these two are building bridges, it creates a basis for reconciliation and a hope that others will do the same."