The European parliament has called on Malta’s prime minister, Joseph Muscat, to quit immediately over his handling of the investigation into the murder of the journalist Daphne Caruana Galizia, as it declared there were “serious and persistent threats” to democracy and the rule of law on the island nation.

In a resolution approved by a large majority, the European parliament said it was deeply concerned about “the integrity and credibility” of the investigation into the death of Caruana Galizia, who exposed the shady financial dealings of Maltese elite and was murdered in a car bombing in October 2017.

The journalist’s assassination has turned the spotlight on Malta’s governing class, raising questions about its record in tackling corruption and money laundering, as well as the sale of “golden” passports that allowed wealthy people to live anywhere in the EU.

While the resolution cannot compel the Maltese government to act, it heaps pressure on the embattled prime minister, who has promised to stand down on 12 January. Two-time election winner Joseph Muscat announced his resignation earlier this month, after it emerged his chief of staff was about to be questioned by police in connection with the case.

The MEP resolution states that anything “whether perceived or real” that compromised the investigation into Caruana Galizia’s murder had to be excluded, but that “this risk [of compromise] persists for as long as the prime minister remains in office”.

A European parliament press statement to accompany the resolution was more direct: “Maltese prime minister should resign now.” But the parliament retracted that statement a few hours later, returning to the more cautious wording of the resolution described by one source as “a very roundabout way of saying he should resign now”.

The resolution was approved by 581 of the 690 MEPs who voted in Strasbourg, with 83 voting against and 26 abstaining.

MEPs also raised concerns about corruption and money-laundering on the island, while lamenting that a makeshift memorial to Caruana Galizia in the Maltese capital was cleared away every day. It called on Muscat to put an “an immediate stop to the near-daily destruction of the makeshift memorial in Valletta”.

The wide-ranging resolution was co-drafted by a cross-party trio of MEPs, who took part in an emergency mission to Malta early this month, after progress into the police investigation prompted the resignation of Muscat’s chief of staff, Keith Schembri.

Schembri, who masterminded two election victories for Muscat, has been arrested and released without charge twice in connection with the case. The prime suspect in the murder, the Maltese tycoon Yorgen Fenech, told a court Schembri gave him updates about the police investigation. Fenech has pleaded not guilty to complicity in the murder and all other charges linked to the case. Schembri has denied all wrongdoing.

The resolution, supported across the political spectrum, states that the parliament “deeply regrets that developments in Malta in recent years have led to serious and persistent threats to the rule of law, democracy and fundamental rights including freedom of the media, the independence of the police and judiciary and the freedom of peaceful assembly”.

The language deliberately echoes that of the EU treaty’s article 7 on the rule of law, which could lead to a member state being stripped of voting rights if a “serious and persistent” breach of democratic values is found.

But the parliament stopped short of triggering the EU sanctions procedure. This procedure, currently being used against Poland and Hungary, is increasingly seen as ineffective, because it relies on EU member states acting against one of their own.

Article 7 “is a cannon without gunpowder”, the German Green MEP Sven Giegold, who co-drafted the resolution, said. “It is wiser to have several shots open rather than start with the loudest weapon and waste it.”

He is calling on the European commission to take the Maltese government to court when it breaks EU law, arguing Brussels should be acting over anti-money laundering controls and passport sales. “The infringement procedures [legal action] are not such a big cannon, but they have gunpowder.”

In a statement following the vote, Giegold said: “The European commission can no longer turn a blind eye to the culture of impunity when it comes to money laundering and corruption in Malta. The newly elected commission must begin dialogue with the Maltese government on the rule of law with a view to commencing article 7 proceedings, if no immediate progress is made from the Maltese side.”

Earlier this week, the EU commissioner for justice, Didier Reynders, urged the Maltese government to speed up work to safeguard the independence of the judiciary, tackle corruption and set up a prosecution service free from any control by the prime minister. These were all identified as problems by experts at the Council of Europe, a separate body to the EU. “Recent controversies have underlined that progress should accelerate,” Reynders wrote to the Maltese justice minister, Owen Bonnici. “Clarity about the steps and timetable ahead would be the best way to make clear that the commitments of the Maltese government to progress will be taken forward.”