The move also deals a blow to French President Emmanuel Macron's efforts to break a stalemate in the crisis-hit country.
The announcement by Adib just under a month after he was appointed to the job under a confessional political system, further delays the prospect of getting the foreign economic assistance needed to rescue the Middle Eastern country from the brink of collapse.
Adib told reporters he was stepping down after it became clear that the kind of cabinet he wished to form was "bound to fail."
Meanwhile, Macron has been pressing Lebanese politicians to form a cabinet made up of non-partisan specialists that can work on enacting urgent reforms to extract Lebanon from a devastating economic crisis worsened by the Aug. 4 explosion at Beirut port.
Commenting on Adib's resignation, an official in the French leader's office described it as "a collective betrayal" by Lebanon's political parties.
Lebanon is in desperate need of financial aid but France, the United States and other international powers have refused to provide funds before serious political reforms are made.
The crisis is largely blamed on decades of systematic corruption and mismanagement by Lebanon's ruling class.
But efforts by the French-supported Adib have hit multiple snags, after the country's main Shiite groups, Hezbollah and Amal, insisted on retaining hold of the key Finance Ministry.
After a short meeting with Lebanese President Aoun on Saturday, Adib said he was stepping down after his efforts hit a dead end.
"I have apologized about continuing the mission of forming a government after it became clear that a cabinet according to the characteristics I had set for it would be bound to fail," he told reporters.
The Lebanese pound dropped against the dollar following his resignation.
Lebanon, a former French protectorate, is mired in the country's worst economic crisis in its modern history. The crisis has been compounded by the coronavirus pandemic and more recently by the Aug. 4 explosion at Beirut's port caused by the detonation of thousands of tons of ammonium nitrate.
The devastating blast killed nearly 200 people, injured thousands and caused property damage and losses worth billions of dollars.
Adib's resignation comes a few days after Aoun himself bluntly told reporters that Lebanon would be going to "hell" if a new government was not formed soon.
In a televised address, he criticized his political allies, the Shiite groups Hezbollah and Amal, for insisting on holding on to the Finance Ministry portfolio in any new government, but also criticized Adib for attempting to form a government and impose names for cabinet positions without consulting with the parliamentary blocs.
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Adib, who was an ambassador to Germany before he took the job on Aug. 31, emerged as a candidate for the post of prime minister after he won the support of former Prime Minister Saad Hariri and three other ex-premiers.
According to Lebanon's sectarian-based power sharing system, the prime minister has to be a Sunni Muslim.
French President Macron has described his initiative including a road map and a timetable for reforms, as "the last chance for this system."