Saad al-Hariri also said that he feared for his life, while fiercely criticizing Iran.
He accused Iran of sowing “fear and destruction” in several countries, including Lebanon.
Saad al-Hariri’s father, former PM Rafik al-Hariri, was assassinated in 2005.
The Hariri family is close to Saudi Arabia, Iran’s regional competitor.
Saad al- Hariri has been prime minister since December 2016, 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 Riyadh.
“I have sensed what is being plotted covertly to target my life.”
Saad al-Hariri also attacked the Iran-backed Shia movement Hezbollah, which wields considerable power in Lebanon.
Addressing “Iran and its followers”, the prime minister said Lebanon would “cut off the hands that wickedly extend into it”.
Iran said the resignation would create regional tensions and rejected Saad al-Hariri’s accusations as “unfounded”.
Saad al-Hariri has made several visits in the past few days to Saudi Arabia, whose leadership is strongly opposed to Iran.
His announcement came a day after a meeting in Beirut with Ali Akbar Velayati, an advisor to Iran’s Supreme Leader Ayatollah Ali Kahmenei.
Taking up the prime minister’s office in 2016, Saad al- Hariri promised a “new era for Lebanon” after two years of political deadlock.
The coalition government Saad al-Hariri led brought together almost all of the main political parties in Lebanon, including Hezbollah.
His father, Rafik al-Hariri, was killed by a bomb in 2005 in an attack widely blamed on Hezbollah.
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