BEIRUT—Lebanon’s Prime Minister-designate Saad Hariri stepped down Thursday, citing “key differences” with the president after nine months of political wrangling that failed to put together a government for the crisis-ridden country. The development is likely to plunge Lebanon further into chaos and uncertainty amid an unprecedented economic breakdown—and also dim prospects for a recovery package from the International Monetary Fund. “It is clear that we will not be able to agree with the president,” Hariri said after a 20-minute meeting with President Michel Aoun. “I have excused myself from forming the government. May God help the country.” After the news broke, protesters—mostly Hariri’s supporters—blocked roads and set fire to tires in several parts of Beirut, decrying the deepening crisis. Troops deployed to break up a protest at the edge of Beirut, firing in the air and using armored vehicles to open roads. Protesters pelted the soldiers with stones. The national …