The two states agreed to normalise ties in December last year.
Candidates have put themselves forward for positions in Libya's upcoming Presidency Council and the offices of prime minister.
The sides agreed this week to set up a "unified executive authority" and hold a constitutional referendum before the planned elections.
The Saudi embassy in Qatar could reopen within days as Riyadh and Doha continue their post-blockade rapprochement.
IS has posted a statement on a militant-affiliated website claiming responsibility for the attack.
Ten more bodies were found in mass graves in war-torn Libya, the country's UN-recognised government said.
Comment: The ideals of the Arab Spring remain out of reach for many. But the quest for freedom, though long and uneven, is inevitable and unstoppable, writes Mohamed ElBaradei.
The United Arab Emirates and Qatar will reopen flights at the end of the month.
The sale of 50 F-35 jets and up to 18 armed drones was promised to the UAE when it agreed to normalise relations with Israel in August.
A spokesman for the Muslim Brotherhood has predicted that Egypt will witness an uprising against the practices of President Abdel Fattah Al-Sisi.