A United Nations commission of inquiry headed by German magistrate Detlev Mehlis is due to deliver its report on 15 September, although the deadline could be extended.
MP Saad al-Hariri, son of the slain billionaire ex-prime minister, has been in Paris for the past two weeks and confided in US television interviews that he felt his life could be under threat.
Druze leader Walid Jumblatt, his main ally, has been camping since their June election victory at his stronghold in the Shouf mountains, southeast of Beirut, and flew off to Paris at the weekend on a private jet.
Several other anti-Syrian ministers and deputies, such as Communications Minister Marwan Hamadeh and Vice President Farid Makari, have joined the exodus to the French capital, according to Beirut newspapers.
Journalists who have come under criticism in the Damascus press, such as Ali Hamadeh, are also among them.
Amid continued tension in Beirut, MP and journalist Gibran Tueini said on Monday he had been informed of a possible hit-list.
"Certain political figures, including myself, are directly threatened," he said.
He had received "a report from Lebanese security officials in which the international commission speaks of the existence of a list of Lebanese political figures who could be assassinated".
Jumblatt is also in Paris
MP Michel Aoun, a Christian leader who emerged as one of the big winners of the polls, in an interview with Al-Balad newspaper spoke of "a plan to assassinate four important Lebanese figures, two Muslims and two Christians".
"The assassination of one of these figures would cause an upheaval on the domestic scene and an uprising," he warned, adding that he could be targeted and had stepped up his personal guard.
Several figures have been assassinated since al-Hariri's motorcade was blown up on the Beirut seafront on 14 February, in an attack the opposition at the time blamed on Damascus despite its protestations of innocence.
Journalist Samir Kassir was killed on 2 June in Beirut and former communist party chief George Hawi on 21 June. Defence Minister Elias Murr escaped an assassination bid on 12 July in which two people were killed.
Last week, the UN Security Council called on Syria to cooperate fully with the international probe into the Hariri murder.
As the inquiry picks up speed, the head of Lebanon's presidential guard, Mustafa Hamdan, and three former pro-Syrian security chiefs were turned over to the UN inquiry commission on Tuesday under arrest warrants.