Pope Francis on Friday  joined the chorus of shock over the car bomb slaying of Maltese investigative journalist Daphne Caruana Galizia, sending a note expressing his condolences to the overwhelmingly Catholic island nation.

In a highly unusual gesture from the Vatican after the death of a private citizen, Francis wrote on Friday to the archbishop of Malta to say he was praying for the journalist’s family and the Maltese people “at this difficult moment” and was “saddened by the tragic death”.

Five days after Caruana Galizia’s death in a powerful car bomb yards from her home in the rural north of the island, an autopsy was being carried out on her body, but police have warned it could take several weeks before the evidence gathered from the site was fully assessed.

The police commissioner, Lawrence Cutajar, told reporters four Dutch forensic experts and four FBI investigators were helping Maltese specialists “because we felt we could have difficulties lifting evidence”. He refused to reveal any further details, describing the situation as “very fragile”.

Cutajar, Malta’s fifth police chief in five years, could not confirm reports that the bomb was triggered remotely. But one of his predecessors, John Rizzo, told local media that it appeared the six car bombings carried out in Malta over the past two years had all used mobile-detonated devices. None have yet been solved.

Several EU leaders gathered for a summit in Brussels called for a full international investigation, while the 53-year-old journalist’s three sons have demanded the resignation of the prime Minister Joseph Muscat and senior officials.

The president of the European parliament, Antonio Tajani, said on Thursday night there was broad agreement among the EU27 on the need for some form of international involvement “to fully clarify an event of unprecedented gravity”.

EU officials and diplomats said Germany, France, Spain and Portugal backed the move, which Muscat said he would welcome. The European parliament will next week debate press freedom in Malta, described by one MEP, Sven Giegold, as “a mecca for money launderers and tax avoiders” with a “culture of impunity”.

Muscat has rejected criticism that the island has allowed wealthy foreigners and international criminal networks to capture its institutions and flout the rule of law. Speaking on the sidelines of the summit he said he would “not exclude any path, any sort of measure, to get to the bottom of this”.

Caruana Galizia, whose hugely popular blog attacked high-level corruption, shady business dealings and organised crime on the island, exposed connections between Muscat’s wife and members of his government to offshore shell companies in Panama. The Muscats have denied the allegations. Caruana Galizia also criticised senior figures in the Maltese opposition.

Her three sons, Paul, Andrew and Matthew – also a prize-winning investigative reporter – have called on Muscat to resign, and to replace the police commissioner and attorney general with “public servants who won’t be afraid to act on evidence against him and those he protects”.

The sons said in a Facebook post they would not endorse a suggestion by Muscat that a “substantial and unprecedented” reward might help find their mother’s killer, saying that identifying the perpetrators was not enough and that corruption had to be rooted out as well.

“We are not interested in justice without change,” they wrote. “We are not interested in a criminal conviction, only for people in government who stood to gain from our mother’s death to turn round and say that justice has been served.

“Justice, beyond criminal responsibility, will only be served when everything that our mother fought for – political accountability, integrity in public life and an open and free society – replaces the desperate situation we are in.” Muscat should “show political responsibility and resign”, they said.