The urgent mission of seven MEPs to the Mediterranean island follows an escalation in the murder case and Prime Minister Joseph Muscat's decision to resign over what critics have called a botched investigation.
"Cooperation in the EU is based on trust and I thought this was very evident to everybody, but that trust has been very seriously damaged," Dutch MEP Sophie in't Veld told journalists after meeting Muscat.
"We'll see what we hear in the next day and a half, but I am not coming out of this meeting with more confidence," she said.
The outgoing prime minister has been accused of obstructing justice by protecting political allies and aides. Last week his chief of staff, Keith Schembri, and tourism minister Konrad Mizzi resigned.
"The problem is not only between the PM and Maltese people. It's also a problem between Malta and the EU," In't Veld said.
Caruana Galizia, a mother of three described as a "one-woman WikiLeaks", was blown up in a car bomb attack near her home in October 2017. She was known for exposing cronyism and sleaze within the country's political and business elite.
Three men are facing trial for carrying out the assassination, but who ordered the murder remains a mystery.
The European Parliament said it would examine doubts about the judiciary's independence and allegations of corruption.
Confidence could only be restored if the truth about the murder was brought to light, In't Veld said.
Caruana Galizia had alleged that Schembri and Mizzi were involved in corruption, claims both men have denied.
Tycoon Yorgen Fenech, arrested as he tried to leave on his yacht, has been charged with complicity in the murder.
Fenech has claimed Schembri was the "real mastermind" behind the killing, according to police sources.
Schembri was arrested last week but released two days later, fuelling accusations of a cover-up.
In't Veld said Schembri's release was "a point of concern".
The delegation was "extremely concerned that somebody whose name pops up in so many different cases is free. That's very difficult to explain to people," she said.
The MEP said investigators were "working very hard", with help from Europol, the European Union's police agency.
"It's not over yet," she added.
One of Caruana Galizia's sons, Andrew, said on Twitter he suspected Muscat had protected chief of staff Schembri for so long because he was "waiting to see whether (he) would be successful in covering up my mother's assassination".
Once "it was clear he failed", Schembri was pushed out, he said.
In a phone call on Monday with Malta's justice minister, European Commission Vice President Vera Jourova "insisted that the investigation has to be brought to conclusion without any political interference," a spokesman said on Tuesday.
She also "expressed her concern regarding the situation in Malta," the spokesman said.