JAKARTA (REUTERS) - Indonesian authorities have rescued 65 asylum-seekers trying to reach Australia after their boat ran aground on a reef, Indonesian police said on Tuesday.

An Australian opposition politician said the boat had run aground after being towed away by the Australian navy, underscoring the risk to migrants of a tough Australian policy.

Migrants crammed into boats have been trying to cross the Mediterranean between Africa and Europe in recent weeks and the Andaman Sea in Asia, highlighting a global issue that many countries are struggling to deal with. Australia has adopted one of the toughest stands against asylum seekers trying to reach its shores by boat, turning back vessels where it is safe to do so and holding indefinitely thousands of others in overseas detention centres.

The boat that ran aground off Indonesia's East Nusa Tenggara province on Sunday was trying to cross to the Australian-controlled Ashmore Reef, Budi Santoso, head of the Indonesian police's asylum seeker taskforce said in a text message.

The boat was carrying 54 Sri Lankans, 10 Bangladeshis, and one person from Myanmar. Three of them were children.

The number of asylum seekers reaching Australia pales in comparison with other countries but it is a polarising political issue on which Prime Minister Tony Abbott has taken a tough line since his 2013 election win.

The boat crashed into the reef after being turned away by the Australian navy, Australian opposition Greens Party Senator Sarah Hanson-Young said in a statement. "Australia's policy of turning back boats continues to put the lives of young children at risk," Hanson-Young said. "While Malaysia, Indonesia and Thailand have ceased turning boats around, the Australian government continues to shirk its responsibilities in the region, putting lives in peril."

Australia uses offshore detention centres in Papua New Guinea and the tiny South Pacific island nation of Nauru to process would-be refugees who often pay people-smugglers in Indonesia for a place on a rickety boat. Many have died trying to reach Australia.