The request comes after Syria's ruling Baath party expelled former vice president Abdel Halim Khaddam after he implicated the regime in Mr Hariri's murder.
Inquiry spokeswoman Nasrat Hassan said a request has been made to Syrian authorities to interview President Assad, along with others, as well as meet with Mr Khaddam "as soon as possible".
It remains to be seen whether President Assad and Foreign Minister Faruq Shara will agree to be questioned, after refusing to meet with the previous inquiry chief Detlev Mehlis.
In a statement carried by the official SANA news agency, the party leadership said Mr Khaddam had betrayed the party, the homeland and the wider Arab nation.
"The national leadership has decided to throw Khaddam out of the party. It
considers him a traitor,” the statement said.
It came a day after Syria’s parliament unanimously voted to try Mr Khaddam for treason over his remarks.
It’s the first time in the regime's history such a high-ranking official had turned whistleblower.
Mr Khaddam, in a television interview broadcast on the Al-Arabiya television network, accused Syrian President Bashar al-Assad of threatening Mr Hariri just months before his murder in February 2005.
Mr Khaddam quoted Mr Assad as telling Mr Hariri during a meeting in Damascus: "I will destroy anyone who tries to hinder our decisions."
Political pressure
A UN report has already implicated Syrian intelligence in the assassination of the billionaire businessman and five-time prime minister.
Mr Hariri’s murder led to heightened international pressure on Syria to end its 29-year military presence in its smaller neighbour last April.
In March, Syria denied a report from a UN fact-finding mission that President Assad threatened Mr Hariri and Druze leader Walid Jumblatt if they opposed the policies of Damascus.
Young Hariri praises Khaddam
Mr Hariri's son and political heir Saad hailed the "historic testimony" given by Mr Khaddam.
Saad Hariri, who heads the majority anti-Syrian bloc in the Lebanese parliament but lives in France and Saudi Arabia for security reasons, said Mr Khaddam's comments “serves the interests of Lebanon and of the truth that the Lebanese people champion."