Immigration ministers have intervened to grant more than 30 visitors visas to foreign tourists to Australia over the past six years.

In the wake of revelations showing Peter Dutton, in 2015, approved visitor visas to an Italian and a French au pair facing deportation, Guardian Australia has examined statements to parliament of ministerial interventions.

The documents show out of the 1,159 ministerial interventions between January 2012 and end of June 2018 the vast majority involved humanitarian (refugee) visas, bridging visas or visas for former residents returning to Australia.

But there are at least 34 people who were granted “subclass 600” visitor visas. No details are given about the circumstances and there are no suggestions they all relate to au pair cases although at least two are known to.

The prime minister, Scott Morrison, said he had been assured Dutton’s decisions had been made in a careful and considered way. And Peter Dutton defended his interventions in 2015, saying they were based on the merit of individual cases according to the law.

Guardian Australia revealed this week that an Italian woman was coming to Australia to work for Dutton’s former Queensland police colleague, and a French au pair was connected to AFL boss Gillon McLachlan’s relatives. Over the next fortnight a Senate inquiry is set to examine Dutton’s use of ministerial intervention.

The au pair was due to work for McLachlan’s second cousin Callum Maclachlan, whose father Hugh had donated $150,000 to the Liberal party since 1999.

The 34 cases of visitor visas that immigration ministers and their assistant ministers, Liberal and Labor, have granted since the start of 2012 include:

· 2018 so far: 53 ministerial interventions – five cases involved visitor visas.

· 2017: 133 ministerial interventions – more than eight cases involved visitor visas but one document said visas were granted to an unspecified number of people.

· 2016: 138 ministerial interventions – nine cases involved visitor visas.

· 2015: 180 ministerial interventions – three cases involved visitor visas (two confirmed related to au pairs).

· 2014: 192 ministerial interventions – three cases involved visitor visas.

· 2013: 242 ministerial interventions – zero visitor visas (Coalition government elected September 2013).

· 2012: 221 ministerial interventions – three cases involved visitor visas (Labor government in power).

Some of the visitor visas were granted for lengthy time periods: then-immigration minister Scott Morrison granted a visitor visa for four years on 5 November 2014, while Dutton granted an unspecified number of people visitor visas for three years on 11 May 2017.

Abul Rizvi, who worked for the immigration department from the early 1990s to 2007, rising to the ranks of deputy secretary, likened obtaining ministerial intervention to “winning the lottery”.

In 2015-16 the immigration department received 5,000 requests for ministerial intervention, documents obtained by Guardian Australia show.

But the department only put 2,000 cases on to Dutton’s in-tray including 716 which were hand-balled to the assistant minister.

But just because the papers get to their desks doesn’t mean they actually have to read them.

Under the Migration Act, an immigration minister can use special discretion powers to intervene in visa cases if they think it is in the public interest to do so.

The minister gets to decide what is in the public interest and is not legally bound to intervene or to even consider intervening.

Ministerial discretion has been around since 1989 and the power was designed to be a “safety valve” for difficult cases that were outside the statutory visa criteria.

While more than 34 tourists have successfully obtained new visas under ministerial intervention, there has been some community anger other cases are struggling to get a hearing with the minister.

There are more than 100,000 signatures on a petition pleading for ministerial intervention for a Tamil asylum seeker family.

Nadesalingam and Priya and their Australian-born daughters were removed from their home in Biloela, central Queensland, in a dawn raid in March and are now in a Melbourne detention centre. Their case is before the federal court.

So far Dutton or the new immigration minister David Coleman have not taken action.

Likewise, military veteran Jason Scanes has tried repeatedly to get an appointment with Dutton to discuss the case of an Afghan interpreter he worked with during his war deployment.

And pleas by Tigers star Dustin Martin to be reunited on Australian soil with his father have fallen on deaf ears. Shane Martin was deported to New Zealand because of a criminal record and association with outlaw motorcycle gangs.

The au pair saga is not the first time there have been controversies over ministerial intervention powers.

During the Howard government, then-immigration minister Philip Ruddock’s use of ministerial discretion in four cases from 1998 onwards was subject to a Senate inquiry in 2003/04.

Ruddock was under fire over “cash-for-visa” allegations.

There were claims visas had been granted to people who had personally or indirectly made donations of up to $100,000 to the Liberal party.

But the inquiry was unable to get to the bottom of the matter because it was not given access to case files.

There were also subsequent reports Ruddock’s successor Amanda Vanstone intervened to grant a suspected mafia figure a visa in 2005. His relatives had previously made donations to the Liberal party. .

Former Labor immigration minister Chris Evans in 2008, expressed discomfort over the ministerial intervention power.

“I have formed the view that I have too much power. I am uncomfortable with that, not just because of concern about playing God, but also because of the lack of transparency and accountability for those decisions and the lack in some cases of any appeal rights against those decisions,” he told a Senate hearing.

After holding an independent review Evans adopted several changes he said were aimed at restoring integrity and transparency.

In light of the so-called au pair affair, the new Senate inquiry may reconsider some of the unused recommendations from the 2003/04 upper house investigation such as publicly naming the ministerial intervention visa recipients and whoever goes in to bat for them.