It comes after the special rapporteur on torture said some aspects violated the convention against torture.
Australia detains all asylum seekers who arrive by boat, holding them in offshore processing camps.
Rights groups have criticised conditions on Manus Island, where asylum-seekers are held.
In a new report to be tabled to the UN Human Rights Council on Monday, the rapporteur, Juan Mendez, investigated allegations of torture and abuse in more than 60 countries.
In Australia, he highlighted some cases where the authorities had failed to provide adequate detention conditions, end the detention of children, or prevent escalating violence and tension at Manus Island.
This meant Australia had violated the right of the asylum-seeker to be free from torture and cruel, inhuman or degrading treatment, the report said.
The Australian government has rejected the report.
When asked about the UN's findings, Mr Abbott told reporters:  "I really think Australians are sick of being lectured to by the United Nations, particularly, given that we have stopped the boats, and by stopping the boats, we have ended the deaths at sea."
He said hundreds had drowned at sea as the people-smuggling trade flourished under the previous government.
Mr Abbott said stopping the flow of people coming to Australia by boat, mostly through Indonesia, was the "most humanitarian, most decent, the most compassionate thing you can do".
"We have stopped the boats and I think the UN's representatives would have a lot more credibility if they were to give some credit to the Australian government for what we've been able to achieve in this area," Mr Abbott said.
When asked about conditions on Manus, Mr Abbott said: "All of the basic needs of the people on Manus Island are being met ... everyone's needs for food, for clothing, for shelter, for safety are being more than met."
One of the allegations investigated by Mr Mendez is the intimidation and ill-treatment of two asylum-seekers after they gave statements about violent attacks at Manus. He found their rights were in fact breached.
He also found that two government changes to immigration legislation risk violating international laws prohibiting torture.
The report found violations in more than 60 other countries including in the US for the 30-year imprisonment of a mentally ill man on death row.
It also raises alarm at the proposed deportation of several individuals from the UK to countries that engage in torture.
Australia asylum: Why is it controversial?

They were seized when the jihadists swept through al-Qaryatain in Homs province, monitoring groups say.
Many of the Christians had fled to al-Qaryatain to escape fighting in Aleppo province to the north.
Islamic State (IS) has treated Christians harshly in other places under its control.
The group follows its own extreme version of Sunni Islam and has previously ordered Christians to convert, pay jizya (a religious levy), or face death.
According to the UK-based Syrian Observatory for Human Rights (SOHR), at least 230 people were seized by Islamic State (IS) fighters in al-Qaryatain.
Some were taken from inside a church, SOHR said. It said IS was hunting down a list of people it suspected of "collaborating with the regime".
The Assyrian Federation of Sweden, whose members have relatives in the town, said about 100 families were being held.
The federation says it has not been able to contact anyone inside the town and the conditions of the captives are not known.
The SOHR said "at least 60" Christians were among those being held.
Earlier this year, dozens of Assyrian Christians were abducted by IS militants in attacks on villages in Hassakeh province in north-east Syria.
A local Christian militia said it believed the captives were taken away to a mountain, but their fate since then is unclear.
Syria's beleaguered Christians
Australian Prime Minister Tony Abbott has said the country is "sick of being lectured" by the UN over its treatment of asylum seekers.
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Islamic State militants have abducted dozens of people, many Christian, from a Syrian town captured on Thursday from pro-regime forces, reports say.