He also said he expected the Maltese authorities "to spare no effort in getting to the bottom of what happened".
"Daphne's murder must not go unpunished," he said.
"How can we credibly claim to defend journalists around the world if we cannot even offer them protection and justice here at home," he added.
Ms Caruana Galizia, 53, had published leaked documents on alleged money laundering cases involving top Maltese officials.
She died when a car bomb exploded as she drove away from her home in Mosta last Monday.
In a statement, two Green MEPs, Eva Joly and Sven Giegold, said: "We want a serious investigation by the European Commission on Malta's respect of the European rules against money laundering."
They also alleged the "Maltese government has failed to take serious action against high level cases of money laundering in its country".
However, EU Justice Commissioner Vera Jourova said in a letter to EU Greens MEPs that "based on the information available so far, there appear to be no grounds to suspect a systematic breach of Union law pertaining to the prevention of money laundering" in Malta.
She added, however, that the Commission has requested more information from the Maltese authorities on recent cases of alleged money laundering involving Prime Minister Joseph Muscat's chief of staff, Keith Allen Schembri.
For years, Ms Caruana Galizia had made detailed allegations of corruption against Mr Muscat's inner circle.
Following her death, her family accused Mr Muscat of filling his office with crooks and creating a culture of impunity.
He had turned Malta into a "mafia island", they alleged.
Malta's government has asked for assistance from the FBI, and from Dutch experts as it examines the case.
Mr Tajani says the European Parliament press room in Strasbourg will be named after Ms Caruana Galizia, in tribute to her.