TV footage showed protesters also breaking into the energy and economy ministries.
They chanted "the people want the fall of the regime", reprising a popular chant from the Arab Spring uprisings of 2011. They held posters saying "Leave, you are all killers".
The US Embassy in Beirut said the US government supported the demonstrators' right to peaceful protest and urged all involved to refrain from violence.
The embassy also said in a tweet that the Lebanese people "deserved leaders who listen to them and change course to respond to popular demands for transparency and accountability".
Prime Minister Hassan Diab said the only way out was early parliamentary elections.
'Go home!'
The protests were the biggest since October when thousands of people took to the streets in protest against corruption, bad governance and mismanagement.
“You have no conscience, you have no morality. Go home! Leave! Resign, Enough is enough,” shouted one of the protesters. “What else do you want? You brought us poverty, death and destruction,” said another.
Soldiers in vehicles mounted with machine guns patrolled the area. Ambulances rushed to the scene.
"Really the army is here? Are you here to shoot us? Join us and we can fight the government together," a woman yelled.
Read also: Lebanese Governments Sets 4-Day Deadline to Find Culprits Behind Beirut Explosion
Tuesday's blast was the biggest in Beirut's history. Twenty-one people were still reported as missing from the explosion, which gutted entire neighborhoods.
The government has promised to hold those responsible to account. But few Lebanese are convinced. Some set up nooses on wooden frames as a symbolic warning to Lebanese leaders.
"Resign or hang," said one banner at the demonstration.
The prime minister and presidency have said 2,750 tonnes of highly explosive ammonium nitrate, which is used in making fertilizers and bombs, had been stored for six years without safety measures at the port warehouse.