Indonesian President Susilo Bambang Yudhoyono spoke to Australian Prime Minister John Howard by telephone on Friday.
It is believed he urged Australia not to grant the Papuans asylum, saying they had nothing to fear back home.
Indonesian Foreign Minister Hassan Wirajuda also said they would not be prosecuted on their return to Indonesia.
The asylum seekers, from Indonesia’s troubled Papua province, were found at Australia's Cape York peninsula over a week ago after sailing for five days in an outrigger boat with a banner accusing the Indonesian military of conducting genocide in their homeland.
The Australian government flew the group, which includes seven children, to a detention facility on Christmas Island, off the north-west coast of Australia.
The families among the group have been put in immigration department housing and the single men in a detention centre.
One man from the group has suspected tuberculosis and has been taken to Western Australia for more tests.
"The president talked on the telephone with Australian Prime Minister John Howard (on Friday). Indonesia stressed our position on the
Papuans (asylum seekers)," Mr Wirajuda told reporters.
"They are not people that we will prosecute according to law.
There is no reason to give them political asylum. Therefore, they should be returned to Indonesia."
Jakarta has warned that relations could be strained if Australia grants the group asylum and Australia has said it considers Papua a legitimate Indonesian territory.
Refugee groups say the Papuans should never have been moved from the Australian mainland and should be given bridging visas while their asylum claims are assessed.
Immigration lawyers will go to Christmas Island on Monday to speak to the Papuans.
Their village area has reportedly been the scene of recent violence during which four people, including a teenage boy, were killed after police allegedly opened fire in a marketplace.
Papuan independence activists have waged a campaign for more than 30 years to break from Indonesia while a low-level armed rebellion has also simmered. Human rights groups have accused the Indonesian military of widespread abuses there.
Jakarta took over Papua from Dutch colonial rule in 1963.
In 1969, its rule was formalised in a United Nations-backed vote by community leaders which was widely criticised as a sham.
Meanwhile, Indonesia's navy has sent two warships to its sea border with Australia to prevent Indonesian fishermen from straying illegally into Australian waters, state news agency Antara reported.