The funeral of an investigative journalist killed in a car bomb near her home in Malta has been held without the presence of top government and opposition leaders, after her family objected to their attendance.

No group or individual has so far come forward to claim responsibility for the attack on 16 October on Daphne Caruana Galizia, who led an investigation into corruption in Malta using the Panama Papers that implicated the government and the opposition.

Mourners included her husband, three adult sons and the European parliament president, Antonio Tajani, but President Marie-Louise Coleiro Preca and the prime minister, Joseph Muscat, were told they were not welcome.

A spokesman for Muscat said: “The family has made it widely known that it does not wish the state authorities to attend.”

The government declared a national day of mourning and flags have flown at half mast.

“We still do not know who killed Daphne,” Archbishop Charles Scicluna told mourners. “Whoever took part, in one way or another, in Daphne’s murder, I have this to tell you: However hard you try to evade the justice of men, you will never escape from the justice of God,” he said. “Repent before it is too late.”

Addressing her fellow journalists, the archbishop said: “Do not be afraid.”

As Caruana Galizia’s coffin was driven away from the church, the crowd broke out singing the Maltese national anthem.

In Brussels, the flag at European commission headquarters flew at half-mast in Caruana Galizia’s memory. The commission issued a statement condemning the “brutal attack” that killed her.

“The right of a journalist to investigate, ask uncomfortable questions and report effectively, is at the heart of our values and needs to be guaranteed at all times,” the statement said.

In a Facebook post written the day after her death, Caruana Galizia’s son, who is also an investigative reporter, said Malta had become a “mafia state”. A week later, thousands of people attended a rally demanding justice.

On Thursday, eight of the world’s largest news organisations urged Frans Timmermans, the European commission vice-president, to investigate the murder, saying it could not be allowed to achieve the “clear objective of silencing her investigation into corruption at the highest levels in Malta”.

The signatories include Katharine Viner, the editor-in-chief of the Guardian, Dean Baquet, the executive editor of the New York Times, and James Harding, the director of news and current affairs at the BBC.

In response to the letter, Timmermans said Malta should leave “no stone unturned” in the hunt for her killers. “We want those directly and indirectly responsible for this horrible murder to be brought to justice,” he said.

Readership of Caruana Galizia’s blogposts often exceeded the circulation of the country’s newspapers. One of her targets was Muscat, whose wife’s name surfaced in the Panama Papers, leaked documents detailing offshore financial accounts maintained by prominent people. Both Muscat and his wife denied wrongdoing.

Muscat has said everything would be done to find Caruana Galicia’s killers. His government has offered a €1m reward and protection for anyone providing information to help identify them.

The journalist’s family has refused to endorse the reward, calling instead for Muscat’s resignation for “failing to uphold our fundamental freedoms” by not rooting out corruption.

Last week, a senior Italian prosecutor told the Guardian that there were possible links between the murder of Caruana Galizia and an Italian investigation into an illicit fuel-smuggling network.

Carmelo Zuccaro, a chief prosecutor in Sicily who is leading the fuel-smuggling inquiry, said he “could not exclude” the possibility that some of the men targeted in his investigation – which spans Libya, Malta, and Italy, and allegedly involves an organised crime network in Sicily – could be behind the murder.