Mr Hariri's father, former prime minister Rafik al-Hariri, was assassinated in 2005.
Mr Hariri accused Iran of sowing "fear and destruction" in several countries, including Lebanon.
He was named prime minister in November last year, after previously holding the position between 2009 and 2011.
"We are living in a climate similar to the atmosphere that prevailed before the assassination of martyr Rafik al-Hariri," he said in the broadcast from the Saudi capital Riyadh.
"I have sensed what is being plotted covertly to target my life."
Mr Hariri also attacked the Iran-backed Shia movement Hezbollah, which wields considerable power in Lebanon.
What is Hezbollah?
He has made several visits in the past few days to Saudi Arabia, whose leadership is strongly opposed to Iran.
Taking up the prime minister's office last year, Mr Hariri promised a "new era for Lebanon" after two years of political deadlock.
Saudi influence at play?
Mr Hariri's resignation has come as a big surprise, plunging Lebanon's often turbulent political scene into new uncertainty.
He has had a complicated political career, moving to and fro between Lebanon and Saudi Arabia - his family's key backer.
His resignation follows recent visits to the Saudis, raising speculation that their influence is likely to be at play.
Certainly, his ferocious denunciation of Iran and Hezbollah, which his own militia once battled unsuccessfully on the streets of Beirut, is in line with Saudi policy.
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