The application - filed by lawyers Jason Azzopardi, Karol Aquilina and Therese Comodini Cachia on behalf of the deceased's family - read that Daphne Caruana Galizia was brutally killed when a bomb in a auto she was driving exploded.
At a press briefing, Joseph Muscat (centre-left), whose close friends and family has been the target of violent attacks by Daphne Caruana Galizia, has denounced an act of "barbaric" and ordered the security forces to concentrate all of their resources. She also wrote a blog called "Running Commentary". Opposition leader Adrian Delia sued her over a series of stories linking him to a prostitution racket in London, and economy minister Chris Cardona claimed libel when she wrote that he visited a brothel while in Germany on government business.
"Everyone knows Ms Caruana Galizia was a harsh critic of mine, both politically and personally", he said.
Malta is the European Union's smallest state and has a population of 400,000.
Maltese President Marie-Louise Coleiro Preca called for calm.
He said: "I will not rest until I see justice done in this case".
Ms Caruana Galizia filed a police report two weeks ago saying she was receiving threats, police told Maltese news outlets on Monday.
The data was obtained by the German newspaper Süddeutsche Zeitung and shared with media partners around the world, including the Guardian, by the International Consortium of Investigative Journalists (ICIJ) in Washington.
European politicians and journalists expressed dismay at Caruana Galizia's death.
Michelle Muscat was accused of being the beneficial owner of a secret Panama bank account, which Caruana Galizia had alleged was used to stash kickbacks from Azerbaijan's ruling family.
Caruana Galizia, 53, had spent the previous year publishing stories about allegations of corruption involving Prime Minister Joseph Muscat and his closest allies.
Caruana Galizia was a fearless journalist and blogger who exposed numerous offshore dealings of prominent figures in Malta.
Mr Muscat said he had asked the U.S. government and the Federal Bureau of Investigation for help investigating the vehicle bombing.
Muscat said her death resulted from a "barbaric attack" that also assaulted freedom of expression.
Caruana Galizia started to contribute regular columns to The Malta Independent and was well-known for her direct style of writing.