The small publication Magazinet said in its online edition on Tuesday that its editor-in-chief, Vebjoern Selbekk, "regretted if the drawings offended Muslims".
Islam considers any image of the prophet blasphemous.
The cartoons, which first appeared in Danish daily Jyllands-Posten last 30 September, included ones showing the prophet wearing a time bomb-shaped turban and portraying him as a knife-wielding nomad flanked by shrouded women.
Selbekk said that Magazinet's reprinting of the 12 cartoons on 10 January was "not aimed at provoking" Muslims and that it was justifiable under freedom of expression laws.
"To regret the use of freedom of expression in a democratic society would damage our democratic foundations," he said.
Selbekk was unavailable for comment on Tuesday, but Magazinet said he had received about 20 death threats amid heavy criticism of Denmark and Norway over the cartoons.
The Norwegian government on Tuesday reiterated that it regretted if Muslims were offended but stressed its belief in fundamental rights.
Prime Minister Jens Stoltenberg told Norwegian daily NTB: "We will not apologise because in a country like Norway, which guarantees the freedom of expression, we cannot apologise for what the newspapers" print.
"We will not apologise because in a country like Norway, which guarantees the freedom of expression, we cannot apologise for what the newspapers" print
Prime Minister, Norway
"But I am sorry that this may have hurt many Muslims," he said.
Anger has spread throughout the Muslim world, with scores of Arab countries, institutions and organisations calling for a boycott of Danish and Norwegian products.
Several ambassadors to Denmark have been recalled and Scandinavians in some Muslim countries have been threatened.
Meanwhile the editor of Jyllands-Posten on Monday apologised for offending Muslims.
"These cartoons were not in violation of Danish law but have irrefutably offended many Muslims, and for that we apologise," editor-in-chief Carsten Juste said in a letter to the Petra news agency in Jordan.