It drew strong criticism among Danish media, which previously had stood united in rejecting calls to apologize for 12 Muhammad cartoons that sparked fierce protests in the Muslim world four years ago.
Prime Minister Lars Loekke Rasmussen expressed surprise at Politiken's move, saying he was worried that Danish media no longer were "standing shoulder to shoulder" on the issue.
Politiken said it did not mean to offend Muslims in Denmark or elsewhere when it reprinted one of the most controversial cartoons, showing Muhammad wearing a turban shaped like a bomb with a lit fuse. Islamic law generally opposes any depiction of the prophet, even favorable, for fear it could lead to idolatry.
Politiken was among several Danish newspapers that reprinted the cartoon in 2008 after police uncovered an alleged plot to kill its creator, Danish cartoonist Kurt Westergaard.
In a statement, Politiken said it "recognizes and deplores" Muslims were offended by the caricature.
"We apologize to anyone who was offended by our decision to reprint the cartoon drawing," it said.
Politiken editor in chief Toeger Seidenfaden told The Associated Press that the paper was apologizing for the offense caused by the cartoon – not the decision to reprint it.
"We have the right to print Kurt Westergaard's drawings, we have the right to print the original 12 drawings, we have the right to print all the caricatures in the world," he said. "We apologize for the offense which the reprint has caused. That is what we apologize for."
Seidenfaden said Politiken considered the statement a "unique chance" to foster a dialogue on the issue and reduce tensions between Denmark and the Muslim world.
Critics blasted the decision.
"Politiken's pathetic prostrating before a Saudi lawyer takes the first prize in stupidity," said Joern Mikkelsen, editor in chief of Jyllands-Posten, which first printed the 12 cartoons.
At Copenhagen newspaper Berlingske Tidende, chief editor Lisbeth Knudsen called the apology "embarrassing and shameful." And Mogens Blicher Bjerregaard, head of the Danish Union of Journalists, said Politiken was "kneeling before opponents of the freedom of press."
Westergaard, who earlier this year had to lock himself inside a safe room when an ax-wielding attacker broke into his home, said he believed the apology was prompted by fear.
"I fear this is a setback for the freedom of speech," Westergaard told AP.
The apology was welcomed by Muslim leaders in Denmark.
"It is beyond any doubt that they have offended some people. It is a nice and human gesture that the newspaper apologizes," said Abdul Wahid Petersen, a moderate imam.
The drawings brought Denmark on a collision course with the Muslim world, with fiery attacks in 2006 against Danish embassies and Muslim leaders demanding an apology from the Danish government, which said it couldn't interfere with Denmark's independent media.
It also put Denmark in the cross-hairs of extremists. Police say they have foiled at least three planned attacks targeting Westergaard or Jyllands-Posten.
The Saudi lawyer representing the Muslim groups, Faisal Yamani, has been demanding apologies from 11 Danish newspapers that reprinted the cartoon. Politiken is the only one so far to have reached a settlement.
"Both parties express their satisfaction with this amicable understanding and settlement, and express the hope that it may in some degree contribute to defusing the present tense situation," Yamani and Seidenfaden said in a joint news release.