The Australian Senate will launch an inquiry into the alleged payments to people smugglers after the Abbott government refused to hand over documents into the claims, citing "public interest immunity".

The inquiry, supported by Labor, will require the government to declare whether any Australian official paid money to anyone on board a vessel from September 2013. If the allegations are true, it will also demand information on who authorised the payments and whether they were legal under both domestic and international law.

The vote comes as Indonesia accused Australia of breaching an agreement on defence, intelligence and border security if it paid people smugglers to return asylum seekers to Indonesia.

Last year Foreign Minister Julie Bishop and her then Indonesian counterpart Marty Natalegawa reaffirmed the Lombok Treaty for security co-operation, after a falling out between the two countries in the wake of the phone tapping scandal.