Hamshahri, one of Iran's five leading newspapers, published the call for cartoons under the title: What is the Limit of Western Freedom of Expression? on its website on Monday.
Davood Kazemi, executive manager of the contest, said the announcement would also appear in the print version of the paper.
"We don't intend retaliation over the drawings of the prophet," he said. "We just want to show that freedom is restricted in the West."
Caricatures of Prophet Muhammad, including one that depicts him wearing a turban shaped like a bomb, have been reprinted in several publications in Europe, the United States and elsewhere in what publishers said was a show of solidarity for freedom of expression.
The images offended many Muslims. Islam widely holds that representations of the prophet are banned for fear they can lead to idolatry.
The drawings sparked protests across the Muslim world, and in some places, including Iran, Syria and Lebanon, the protests turned into attacks against Danish and other Western diplomatic missions. In Afghanistan, nearly a dozen people were killed in protests.
"We expect those papers who published the cartoons to reproduce the cartoons which will be selected during our competition"
executive manager of the newspaper contest
Kazemi said: "We expect those papers who published the cartoons to reproduce the cartoons which will be selected during our competition. Even Israeli cartoonists could send their works to the contest."
He noted, however, that the paper would not accept any insulting cartoons. He did not elaborate.
The call for drawings, in English and Farsi on the website, said that in the West, it was "an unforgiven crime" to debate and review issues such as "looting and crimes perpetrated by the US and Israel, as well as alleged historical events like the Holocaust".
It said the paper was soliciting contributions on the theme of the Holocaust and the limit of Western freedom of expression.
"In the wake of the publication of the profane cartoons in several European newspapers, Hamshahri is going to measure the sanctity of freedom of expression among the Westerners," the announcement said.
The deadline for entries is 5 May. Each contestant can enter up to three submissions.
Many Iranians angrily protested
over the Danish cartoons
"Some weeks after the deadline we will announce the results of the competition," Kazemi said. "Select cartoons will be reproduced in a catalogue and the works will go on public display."
The contest was co-sponsored by the House of Caricatures, a Tehran exhibition centre for cartoons.
Both are owned by the Tehran Municipality, which is dominated by allies of Mahmoud Ahmadinejad, the Iranian president, who is well known for his opposition to Israel.
Kazemi stressed that the government has nothing to do with the contest.
"Government authorities did not affect decision-making process for holding the contest. The idea was independently initiated by the paper," Kazemi said.