Judge Luiz Fux has ordered Battisti's arrest "with a view to extradition", following a request by public prosecutor Raquel Dodge who took office in September.
The former far-left activist, now 63, was sentenced to life in prison in 1993, having been found guilty of the murder of a police officer and a prison guard and complicity in the murder of two shopkeepers.
At the time of the killings he was a member of Armed Proletarians for Communism (PAC), a far-left organisation like the Red Brigades that carried out attacks, kidnappings and assassinations during Italy's "Years of Lead" in the late 1960s and the 1970s.
Fled to France
Like many of today's jihadists, he joined the group in jail, while serving time for armed robbery, and claims to have renounced political violence in 1978, after the murder of Italian prime minister Aldo Moro.
He was arrested in 1979 and sentenced to 13 years in prison for membership of an armed gang.
But his comrades sprung him from jail in 1981 and he fled to Mexico, then to France.
Under the presidency of Socialist François Mitterrand, France refused to extradite left-wing former terrorists to Italy if they had renounced violence, so Battisti was able to find work as a concierge and started writing thrillers based on his experiences.
In the meantime, he had been retried in his absence in Italy and, largely on the basis of the testimony of a captured PAC leader, found guilty on the murder and complicity charges.
The court sentenced him to life with no possibility of release.
Flees to Brazil
France's policy changed in 2004 after the election of right-winger Jacques Chirac to the French presidency and Battisti was arrested with a view to extradition.
Fellow crime writers and other intellectuals, including philosopher Bernard Henri Lévy, launched a defence campaign, which was widely supported on the French left.
Battisti then went underground again, claiming later that the French secret services helped him do so, and fled to Brazil, where he has lived ever since.
In 2007 he was arrested in an operation involving both Brazilian and French police.
Italian newspaper Le Republicca claimed then interior minister Nicolas Sarkozy had known of the fugitive's whereabouts since 2006.
Battisti's supporters accused Sarkozy of greenlighting the arrest to help his successful bid to become French president, a charge that Sarkozy denies.
Italy applied for extradition but then president Lula Da Silva blocked the move on the last day of his term in office, 31 December 2010
Bolsonaro promises extradition
With Lula standing to be reelected this year, before being jailed on corruption charges, Battisti became an election issue.
Far-right candidate Jair Bolsonaro promised that he would no longer be protected and, when he won the election, Italy's far-right deputy prime minister Matteo Salvini called on him to stand by that promise.
The idea that "a man sentenced to life in prison is enjoying life on the beaches of Brazil provokes indescribable annoyance in me", he declared on Monday.
Battisti's lawyer, Igor San'Anna Tamasauskas, told the AFP news agency that he had not received Judge Fux's ruling on Friday morning.