The Solomon Islands has been accused of sheltering its new chief legal officer who is facing extradition to Australia on child-sex charges.
Mr Downer called on the Solomons to hand over Julian Moti
Australian foreign minister Alexander Downer said Julian Moti was hiding at the Solomon Islands High Commission in Port Moresby, Papua New Guinea.
Mr Moti was arrested in PNG on Friday and released on bail. He failed to make his court appearance on Saturday.
The arrest further strained ties between Australia and the Solomons.
Last month, Solomons' Prime Minister Manasseh Sogavare expelled Australia's most senior diplomat for alleged interference in the country's domestic affairs.
Australia has been urging its citizens in the country to "exercise a high degree of caution" as political tensions have risen ahead of the resumption of parliament in the Solomon Islands on Monday.
The opposition had been due to call for a vote of no-confidence in Mr Sogavare's government, but it has been put off until later in the week.
On Saturday, an Australian church official was badly wounded after his mission in the Solomons' capital Honiara was attacked by a mob.
It was unclear if the attack was as a result of growing gang violence in the Solomons or because of deteriorating relations with Australia.
Julian Moti was initially thought to have fled Port Moresby after failing to appear in court on Saturday.
But Mr Downer said it was now apparent he was at the Solomons' offices in the PNG capital.
"We'll hope that the Solomon Islands government does the right thing here," he told reporters in Australia.
"I don't think somebody facing child sex charges should be protected in anybody's embassy or high commission anywhere in the world."
Julian Moti, an Australian citizen of Fijian descent, was on his way to Honiara last week to take up his new job as attorney-general when he was arrested at PNG airport at the request of Canberra.
The Australian authorities want to extradite him to face prosecution over an alleged child sex offence in Vanuatu.
His arrest prompted fierce protests from Honiara. PM Sogavare accused Australia of a "serious violation of the sovereignty of the Solomon Islands".
Mr Sogavare came to power after riots in the Solomon Islands in April.
He expelled Australia's high commissioner Patrick Cole in September, accusing him of interfering in an investigation into the riots.
Canberra wants the Honiara government to cancel the investigation amid fears it will be used to exonerate two pro-Sogavare lawmakers.
Australia has deployed security forces in the Solomons since 2003, when it was invited there by the government to restore order after the country came close to collapse.