You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
"This is a case of extraordinary importance which requires extraordinary measures," the government said in a statement.
Prime Minister Joseph Muscat had told parliament on Wednesday the government would offer a "substantial" reward to anyone with information about the crime but did not say how much would be paid.
Caruana Galizia, who regularly criticised Muscat in her popular blogs, was killed on Monday by a bomb, which tore apart her car as she was driving away from her home on the southern Mediterranean island.
The journalist ran a popular blog in which she relentlessly highlighted cases of alleged high-level corruption, targeting politicians from across party lines, including Muscat.
On Thursday the Caruana Galizia family said they had been informed of the government's plans for a reward but they were refusing to endorse it.
"We are not interested in justice without change," Caruana Galizia's sons Matthew, Andrew and Paul said.
"Justice, beyond criminal liability, will only be served when everything that our mother fought for – political accountability, integrity in public life and an open and free society – replaces the desperate situation we are in," they said.
They also called on the prime minister to resign and said his last act before doing so should be to replace the Police Commissioner and the Attorney General for failing to act over their mother's claims of corruption.
A group of NGOs called the "Civil Society Network" is planning to hold a national protest against the killing on Sunday.