This comes almost a month after he was appointed to the position.
Adib stepped down on Saturday after struggling for more than a month to create a non-partisan cabinet.
Lebanon is bankrupt, with its currency plunging to a fifth of its previous value against the dollar; anti-government protests have persisted for nearly a year; an explosion last month at Beirut's port, blamed ultimately on endemic corruption and mismanagement by Lebanon's venal political class, killed hundreds and leveled whole neighborhoods.
"It is indispensable to have a government capable of receiving worldwide aid", the unnamed official said.
"I apologise to the Lebanese people. for my inability to realise its aspirations for a reformist team", he said.
At a rare news conference devoted to Lebanon, Macron launched an extraordinary diatribe against a Lebanese political elite who he said had looked to their own selfish interests rather than those of their country.
Lebanon is in desperate need of financial assistance but France and other worldwide powers have refused to provide aid before serious reforms are made.
The announced by Adib deals a blow to French President Emmanuel Macron's efforts to break a risky stalemate in the crisis-hit country.
According to observers, the Shiite allies dug in their heels after recent United States sanctions were imposed on a minister of the Amal party and two companies affiliated with Hezbollah.
Malta Claims Fossilized Shark Tooth That David Attenborough Gifted Prince George
Photos released by the palace over the weekend showed the seven-year-old prince looking intrigued as he looked at the tooth. He is very interested in fossils. "I am determined to direct a change in this attitude", the minister said.
He wished his successor well in the "hard task" of forming a government.
After a short meeting with Aoun on Saturday, Adib said he was stepping down after his efforts hit a dead end.
The street value of the Lebanese pound, which has plunged since the economic crisis erupted previous year, weakened further after the news.
Even before the devastating Beirut port blast, the country was mired in its worst economic crisis in decades, its entrenched political class facing widespread popular discontent.
Lebanon defaulted on paying back its debt for the first time ever in March. Talks with the International Monetary Fund on a bailout package have stalled. It killed almost 200 people, injured thousands and caused losses worth billions of dollars.
"When will you finally stop playing your usual games, listen to the cries and needs of the people, prioritize the future of Lebanon?" he posted in Twitter.
Macron had repeatedly pressed Lebanon's leaders to form the government, saying a reform-minded cabinet was essential if aid was to flow in to rebuild the country.
Lebanon's interim prime minister has resigned amid problems in forming a nonpartisan cabinet to lead the country. When asked whether sanctions were on the table, he said he would only consider them at a later stage in conjunction with other powers because he could not see their use for now.
Anti-government demonstrators have staged mass rallies over the past year, calling for a complete overhaul of the political system.