Malta’s prime minister, Joseph Muscat, should resign immediately to avoid risks of political interference with the investigation into the murder of journalist Daphne Caruana Galizia, the European parliament told EU leaders on Thursday.

Muscat, who is under fire over his role in the investigation, arrived at a summit of EU leaders in Brussels on Thursday.

The embattled leader has promised to stand down in January after his Labour party has elected a replacement, despite calls from protesters in Malta and MEPs that he should go sooner.

In a letter delivered to leaders of EU countries as they met in Brussels on Thursday for a summit, the European parliament urged leaders to take a stance, saying a politicians involved in a mission to the island had found the situation “alarming”.

The politicians wrote that Muscat‘s delayed resignation “constitutes a serious risk, real or perceived, the murder investigation and connected investigations will be compromised”, the politicians wrote.

Before the summit, dozens of people demonstrated in front of the Maltese permanent representation to the EU against Muscat‘s participation in the summit. They shouted “shame on you!”, while holding an image of Muscat with the word “murderers” on it. They plastered a wall in front of the headquarters of the European commission with the same image.

In an open letter to EU leaders, a coalition of media and transparency groups also called on them to take a stand in the case. The letter signed by 12 groups including the European Centre for Press and Media Freedom, Reporters Without Borders and Transparency International.

It stated: “Our organisations now call on European Union leaders to urge prime minister Muscat to guarantee that all investigations and legal proceedings will be conducted impartially, promptly and effectively, and without any involvement or influence at all from any individual potentially implicated in the case.”

Separately, civil society activists in Malta have urged the EU “to take a position on the desperate situation in Malta” in an open letter addressed to Charles Michel, the president of the European council, who is chairing the summit. “If the European Union does not reach out to help its own when democracy is being threatened, then we truly will start questioning what is the point of the European Union if it does not practice what it preaches,” states the letter by Occupy Justice, a pressure group of women that formed soon after the investigative journalist’s murder in October 2017.

Facebook Twitter Pinterest Malta’s prime minister, Joseph Muscat, arrives at his office before a meeting with members of the European parliament on 3 December. Photograph: Vincent Kessler/Reuters

In reality, it is unlikely EU leaders will get involved, as they mostly steer clear of anything deemed to be domestic politics in another member state. Muscat was photographed shaking hands with EU leaders at the summit later on Thursday.

The new European council president, Charles Michel, has promised that “the EU, its institutions and agencies will do everything within their power to ensure … that justice is done”. He made the pledge in a letter to Matthew Caruana Galizia, one of the murdered journalist’s three sons, who had contacted him.

Michel said he was deeply shocked by the assassination and expressed a wish to meet Caruana Galizia and his family in Malta, according to extracts of the letter seen by the Guardian. Michel spoke to Muscat by phone on Wednesday but officials were unable to say whether he had raised the Caruana Galizia case.

A senior EU diplomat said he expected Muscat to raise the latest developments in Malta over the dinner: “That is the norm with leaders when it comes to domestic matters.”

Muscat’s presence at the dinner table could prove awkward. Senior EU figures have been shocked over the case of the murdered journalist, who was assassinated in a car bombing in October 2017.

Muscat, twice elected as Malta’s prime minister, came under intense pressure as the investigation into the murder gathered pace in late November, raising questions of a cover-up.

His close confidante and chief of staff, Keith Schembri, resigned when it emerged that a businessman accused of complicity in the murder was about to make allegations against him. Schembri, who denies all wrongdoing, has been arrested and released without charge in connection with the investigation.

The businessman, Maltese tycoon Yorgen Fenech, has been charged with complicity in the killing. He has pleaded not guilty to that charge and four others, including membership of a criminal gang. Fenech told a court that he received regular tipoffs about the investigation from Schembri, as well as advice on what to say in interrogations.

Muscat has insisted he cannot tamper with the police investigation but his protestations failed to convince a visiting group of MEPs. The group said last week that the integrity of the investigation was at risk while Muscat was in office.