Mr L'Estrange, who heads the Department of Foreign Affairs and Trade, was expected to meet with a top Indonesian presidential advisor at the state palace in Jakarta, but a spokeswoman for the Australian embassy said the venue was changed to an unknown location.
"The meeting is on but it is closed to the media," she said in an SMS message to AAP.
She said the president's office insisted upon the change.
Indonesia's Chief Foreign Affairs spokesman Yuri Thamrin, who also heads Australian affairs, said he knew nothing of the talks.
Mr Thamrin said as far as he knew, Mr L'Estrange was only expected to meet with Foreign Minister Hassan Wirajuda.
Mr Wirajuda said he appreciates Australia's move to strengthen its immigration laws, but told the ABC he wants to know what action will be taken on the Papuan refugees.
Mr L'Estrange arrived in Indonesia in an attempt to heal the rift that began when Australia granted asylum to 42 refugees from Indonesian Papua.
Australian Prime Minister John Howard said Mr L'Estrange is presenting the Australian government's views on Indonesian sovereignty of West Papua and informing the Indonesians of changes to Australia's immigration policy.
But he said he doesn't expect the talks will immediately resolve the stand-off.
"These things proceed in an orderly way and it's always a good idea to have these very suave diplomatic foreign ministers handle these things," he said.