* Australia PM tries to revive Malaysia refugee plan
* Second boat sinks in less than a week between Indonesia and Australia
* More than 120 rescued, up to 10 may be missing (Adds political moves, 123 rescued)
CANBERRA, June 27 (Reuters) - The sinking of a second refugee boat between Indonesia and Australia's Christmas Island in less than a week prompted on Wednesday Australia's prime minister to try to revive a people-swap deal with Malaysia and end an impasse on asylum seekers.
More than 120 people were rescued and up to 10 were missing after a crowded boat sank on Wednesday in the Indian Ocean on its way to Australia, less than a week after about 90 asylum seekers died when their boat sank in the same area.
The latest sinking prompted Prime Minister Julia Gillard to suspended parliamentary business to debate compromise laws which will revive her Malaysian agreement and allow for an opposition plan to process asylum seekers on the Pacific island nation of Nauru.
"In view of these events and in view of the events of last week, I want to say to the parliament now most sincerely that I believe the time for the party divide on this issue is at an end," Gillard told parliament.
Gillard has an agreement with Malaysia to send 800 asylum seekers to Malaysia to have their claims assessed, in return for accepting 4,000 asylum seekers who are found to be genuine refugees.
The conservative opposition, however, has opposed the Malaysian option because Malaysia has not signed the U.N. refugee convention.
Refugee policy and border protection are a hot-button issue in Australia, despite the fact the country only receives a small number of the world's asylum seekers each year.
The U.N. refugee agency said Australia received 11,800 claims for asylum in 2011, compared with 441,000 claims globally, with 327,000 of those claims in Europe.
This year, more than 50 boats carrying more than 4,000 asylum seekers have been detected by Australian authorities.
Gillard said 123 people had been rescued from the latest boat, which could have been carrying up to 133 people.
Australia's Maritime Safety Authority released a photograph of the boat before it capsized which showed a heavily crowded vessel, which looks like it is made of timber. The boat was about 200 km (125 miles) north of remote Christmas Island and 185 km (115 miles) south of Indonesia.
The waters between Indonesia and Christmas Island are a common route for asylum seekers, who transit through Indonesia with the help of people smugglers.
The trip is often dangerous. In December 2011, as many as 200 people died when an overcrowded boat sank off the coast of East Java. In 2010, 50 asylum seekers died when their boat was thrown onto rocks at Christmas Island.