Australia said that so far it has attracted 170 applicants to a new program to develop foreign investment by offering overseas millionaires the right of residency in return for a portion of their wealth, in a bid to help the country compete better against other nations for money and expertise from abroad.

The so-called significant investor visa was launched in November. If all those made so far are accepted, the applications, believed to be mostly from China, would translate into inbound investment of at least 850 million...