When 45-year-oldPeter Magyartook to the podium in parliament on Saturday to deliver hisfirst speech as Hungarys new prime minister, he had one message: theViktor Orbanera and the network of loyalists who helped sustain it was over.

He then renewed his calls for President Tamas Salyok to resign, alongside a string of other Orban-appointed figures occupying key judicial and oversight bodies. Its time to leave with some dignity, while its possible, Magyar said, handing them a May 31 deadline to do so.

Magyar, whose centre-right Tisza party last month swept Fidesz from power in a landslide election victory, has made no secret of the fact that he intends to tear down the opposition-proof state his predecessor had spent more than 15 years building.

Zsolt Kerner, a Budapest-based journalist for theHungarianonline news outlet 24.hu, said Magyar had gone to the polls vowing justice, and that he was now dead-set on delivering it.

He seems like a very hard-headed guy, he said. The first, second and third tier [of Orbans network] should be very afraid, he said.

Read moreDismantling Orbans legacy: the reforms that lie ahead for Hungary

From wanted politicians to billionaires

Magyar has also made it clear that under his rule, Hungary will no longer serve as a safe haven for corrupt officials or political allies fleeing prosecution.

Polands former justice minister Zbigniew Ziobro was one of the first who appeared to take the threats seriously. On Sunday, barely 36 hours after Magyar had taken office, Ziobro confirmed he had fled Hungary.

Im in the United States, hetold right-wing Polish broadcaster Republika. I arrived yesterday, and this is my third time travelling around the country.

Ziobro was granted asylum in Hungary last year after facing a string of charges in Poland, including abuse of power, leading an organised criminal group and allegedly diverting public funds to purchase spyware to monitor political opponents. If he is convicted, he could face up to 25 years in prison.

According to media reports, US PresidentDonald Trumphimself granted Ziobro the American visa.

Kerner said that Ziobro likely would have been among Magyars first targets not least because he is keen to repair ties with both Polands EU-friendly Prime MinisterDonald Tuskand theVisegradgroup. Relations within the key eastern alliance which also comprisesCzech RepublicandSlovakiadeteriorated sharply under Orbans rule due to his pro-Russia stance.

IfPolandrequested it, Magyar has already said he would hand them over, he said, referring to both Ziobro and his former deputy, Marcin Romanowski, who was also granted asylum under Orbans government.

Kerner said figures who amassed vast fortunes under the former government including businessmen widely viewed as proxies for the old regime could also soon come under pressure.

In the weeks running up to Magyars installation,The Guardian reportedthat several former Orban associates had allegedly begun transferring their riches out of the country for fear of the incoming leaders vow to crack down on corruption.

Some were also looking into US visa options, hoping to find work at Maga-linked institutions, the paper wrote.

Changing the constitution?

But Magyars bigger challenge, said Zsuzsanna Vegh, a political analyst at the German Marshall Fund, will be to dismantle the vast network of allies that Orban placed and still has in state institutions, like the president, the heads of the public prosecution office and the state audit office.

Just because Magyar calls on these people to resign, it doesnt mean they have to, she said.

If they do not, then I think we can expect that there is going to be a legal battle. Constitutional changes will need to be made to be able to remove these people from office.

One thing, however, that Magyar has demonstrated even before he officially became prime minister on Saturday is that he likes to move fast. That in itself could be a gamechanger,Vegh said.

Given that the deadline that Magyar gave for these people to resign is [already] at the end of May, I expect that Tisza has a very clear roadmap for how to move ahead should they decide to remain in office beyond this deadline.

Vegh said that the system Orban once built to secure his rule has already started to crumble.

The election in April showed that Orbans strategy no longer works, she said. His system was to a large degree built on loyalty andcorruptionand patronage, but also on the belief that he is not defeatable. Then that belief was broken by the evidence that he is.

Originally published on France24