Relations between Indonesia and Australia have soured further after an Australian newspaper published a cartoon lampooning Indonesia's leader.
President Yudhoyono's spokesman said the cartoon was "in poor taste"
Indonesia said the drawing, apparently depicting the president and a Papuan as fornicating dogs, was "not helpful".
It followed the publication in an Indonesian newspaper of a cartoon depicting Australia's prime and foreign ministers as copulating dingoes.
Tensions arose after Canberra decided to give visas to Papuan asylum seekers.
The group of 42 Papuans arrived in Australia by boat in January, saying they were fleeing abuses by Indonesia's military in the restive province.
Indonesia recalled its ambassador, saying it was "surprised and disappointed" by the decision.
'No offence intended'
The cartoon, in The Weekend Australian, depicts what appears to be Indonesian President Susilo Bambang Yudhoyono in the guise of a dog mounting another dog, apparently depicting a Papuan.
The smiling "Yudhoyono" says: "Don't take this the wrong way", above a caption that reads: "No offence intended".
The cartoonist, Bill Leake, told the BBC the work was not intended to depict the Indonesian president.
But he said it was in response to the cartoon which appeared in Indonesia's Rakyat Merdeka newspaper last week.
That cartoon portrayed Australian Prime Minister John Howard and his Foreign Minister Alexander Downer as mating dingoes, with Mr Howard saying: "I want Papua!! Alex! Try to make it happen."
'Tasteless and grotesque'
Australia joined Indonesia in criticising Mr Leake's drawing.
"From a personal perspective, I find the cartoon tasteless and offensive and see no merit of any kind in its publication," Mr Downer said in a statement.
President Yudhoyono's spokesman, Andi Mallarangeng, said the cartoon was "in poor taste", adding that the publication of such images by newspapers "demonstrates the level of their quality".
On Thursday, Mr Downer condemned the Rakyat Merdeka cartoon as "tasteless and grotesque".
Mr Howard, however, said he was unfazed.
"I've been in this game a long time. If I got offended by cartoons - golly heavens above, give us a break," he said, adding that he planned to visit Indonesia soon.