John Brennan said he did not know who was to blame for the murder of Mohsen Fakhrizadeh, as Tehran pointed its finger at Israel.

"This was a criminal act & highly reckless. It risks lethal retaliation & a new round of regional conflict," Brennan said in a series of tweets.

"I do not know whether a foreign government authorized or carried out the murder of Fakhrizadeh," he said.

"Such an act of state-sponsored terrorism would be a flagrant violation of international law & encourage more governments to carry out lethal attacks against foreign officials."

Brennan noted that Fakhrizadeh was not a designated terrorist nor a member of Al Qaeda or the Islamic State group, designated terror groups which would be legal targets.

A strong critic of President Donald Trump, Brennan urged Tehran to "resist the urge" to retaliate and "wait for the return of responsible American leadership on the global stage," a reference to November 3 election winner Joe Biden, who will replace Trump on January 20.

Brennan was director of the CIA from 2013 to 2017, under the administration of president Barack Obama and then-vice president Biden.

Brennan did not take part in Biden's election campaign and has not appeared to be involved in his preparations for taking office on January 20.

But early this week Biden named Brennan's former deputy director at the CIA, Avril Haines, as his director of national intelligence.