The federal integrity watchdog has received 17 referrals a day in its first month of operation.

The National Anti-Corruption Commission, which began its work on July 1, has so far received 541 referrals for investigation.

The commission said about one in eight of the referrals related to matters “well publicised in the media”.

In a statement released on Tuesday, the commission said it appreciated the high level of interest so far, but noted it had decided not to further pursue a number of them.

“We are now reaching out to individual referrers where we need additional information, or to let them know if we have decided not to proceed further,” the commission said.

“We are unable to proceed with referrals where they do not involve a Commonwealth public official, they do not raise a matter of corrupt conduct, (or) they are otherwise not within the commission’s jurisdiction.”

Opposition Leader Peter Dutton on Monday proposed the NACC investigate the way his former department of home affairs managed offshore detention contracts.

But the government has instead set up an independent investigation led by former top bureaucrat Dennis Richardson.

Government Services Minister Bill Shorten is awaiting advice from his department on referring a matter relating to former coalition minister Stuart Robert to the NACC.

– AAP