Responding to calls he step down, Mr Aoun told French TV station BFMTV in his first interview with foreign media since the August 4 blast that it would be “impossible” because it would create a power vacuum.
The interview aired late on Saturday.
The cause of the fire that ignited nearly 3,000 tons of ammonium nitrate stored at Beirut’s port remains unclear.
Documents have emerged showing the country’s top leadership, including Mr Aoun, and security officials were aware of the chemicals that had been stored there for years.
The blast killed 180 people and wounded more than 6,000. At least 30 people are still missing.
Mr Aoun said the investigation is divided into three parts.
The first aims to determine the circumstances surrounding the cargo, the second where it came from and who shipped it and the third who was responsible for handling and securing it.
“We had the determination to reach conclusions quickly but we found out that the issues are very complex and require time,” the president said.
When asked about what measures he took when he learned of the explosives in July, Mr Aoun said the information came to him “very late” but his military adviser was reassured those with direct responsibility were handling the matter.
“They all were informed,” Mr Aoun said, adding he made sure those who could take measures to secure the area were in the loop.
Mr Aoun said FBI and French investigators are helping because “they more than us have the capability and ability to find out the details of what got the ship here, what is the source and who owns it”.
The president, who is backed by the powerful Hezbollah militia, said he asked for satellite images to determine if there was an air raid, saying he has not ruled out the possibility of a foreign missile attack.
Hezbollah leader Hassan Nasrallah has denied his group has any role in the explosion and said any international probe would likely seek to clear Israel of responsibility in the port explosion, if it had a hand.
Israel has denied involvement and so far no evidence has emerged to suggest otherwise.
Many Lebanese want the probe taken out of the hands of their government.
Under pressure, Lebanon’s government resigned on August 10.
For now, there are no formal consultations under way on who will replace Hassan Diab as prime minister and no likely candidate has emerged.
Asked about the public anger, Mr Aoun said he shares the rage.
“They call me the father of the people,” he said.
“I am one of them.”
But Mr Aoun said “it is impossible” for him to step down because it would create a power vacuum.
He also said the moment is not right to hold presidential elections.
“The political and popular atmosphere can’t take new elections before restoring calm,” he said.
“They would be emotional and not a true representation of the people.”
Mr Aoun was elected in 2016, breaking more than two years deadlock in which Lebanon remained without a president.
In light of the deal between the Israel and United Arab Emirates, Mr Aoun did not rule out that Lebanon may one day make peace with Israel as well.
Asked if Lebanon too would reach a peace deal, he replied: “We have problems with Israel that we need to solve first.”
Lebanon and Israel are technically still at war and Hezbollah has engaged in occasional clashes along the border.
They last engaged in a full-fledged conflict in a 50-day war in the summer of 2006.
The UAE and Israel opened diplomatic ties as part of a deal brokered by the US that required Israel to halt its contentious plan to annex West Bank land sought by the Palestinians for a future state.
