Malta has appealed to the Federal Bureau of Investigation and to European forensic experts to help investigate the killing.
"My mother was assassinated because she stood between the rule of law and those who sought to violate it, like many strong journalists", Matthew Caruana Galizia said on Facebook.
Ordinary Maltese called for a strike to demand that whoever was behind Monday's bombing be found and brought to justice.
Graffiti quoting the last words she wrote - "There are crooks everywhere you look" - were written on one of Malta's major roads Tuesday.
Some EU politicians are pressing for closer scrutiny of the tiny European Union nation in the Mediterranean Sea, which is considered a banking haven.
Earlier, the son of Malta's best-known investigative journalist said his mother was killed by a vehicle bomb because of her work exposing political corruption.
Maltese Prime Minister Joseph Muscat was the target of accusations by Galizia in a case linked to the revelations of the Panama Papers.
After the death of the journalist Mr Muscat sentenced her murder, calling it an attack on freedom of expression in Malta.
Among her stories were investigations based on the Panama Papers leak detailing politicians' secret offshore holdings. Muscat and his wife deny they held such companies.
Two weeks before she died, she told police she had received threats.
Besides writing for The Malta Independent, she was a columnist for The Sunday Times in the early 1990s. Her English-language "Running Commentary" blog would often get more readers than all of the Maltese newspapers, for which she also occasionally wrote.
Ms Caruana Galizia had been sued for libel over articles she wrote for her blog.
Prime Minister Joseph Muscat said in his public address 90 minutes after the auto bomb exploded that he had asked the United States for assistance in the investigation.
Speaking to Italian state television Tuesday, the prime minister noted that Caruana Galizia had written about him for years.
He is a journalist-as a data scientist in the worldwide consortium of investigative journalists. He could not impose such protection as he would have been accused of spying on people.
In what could be an unprecedented move in Maltese crime history, Muscat confirmed he is seriously considering the possibility of offering a substantial monetary reward to people who come forward with information which could help the police arrest Caruana Galizia's murderer.
"I condemn the murder of Daphne Caruana Galizia", said Irinia Bokova.
"Everyone knows Caruana Galizia was a harsh critic of mine, both politically and personally, but nobody can justify this barbaric act in any way". More recently she had expanded her criticism to include the opposition Nationalist Party.
The Panama Papers journalist killed by a bomb in her auto signed off her last blog post with a warning which seems chilling in hindsight.
"Daphne played a vitally important role in unearthing serious allegations of money laundering and corruption in Malta, including those involving senior figures in the Maltese government", said Sven Giegold, a Greens member in the European Parliament.
The pledge was dismissed by the victim's son, who said one of the police officers involved in investigating the murder had celebrated his mother's death online.
The European Commission said it was horrified by what it termed probably a "targeted attack".