The four states accuse Qatar of disrupting regional security by supporting Islamist opposition groups and extremists.
"It would be preferable if the parties could engage in a process of de-escalation, one that is indispensable so that negotiations can take place in a constructive atmosphere", Le Drian said in Abu Dhabi. During Tillerson's recent trip, the United States did not offer any extraordinary initiatives or plans that would guarantee the settlement of the crisis.
Le Drian's visit will follow similar trips made by his counterparts from Germany and Britain in recent weeks.
Qatar denies the charges of extremism and called the demands "unrealistic". For that reason, six Arab nations now boycotting Qatar have called upon Federation Internationale de Football Association to cancel the 2022 bid of Qatar and award the games to another nation.
Despite the blockade by the four Arab countries, life has not been impacted significantly in Qatar.
Speaking after meeting Al Thani, Turkish Foreign Minister Mevlut Cavusoglu said the demands to close the base "go against the two countries' sovereignty".
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Mr Le Drian said France counted on "reinforcing co-operation with Qatar in the fight against terrorism, particularly in combating terrorism financing".
Mr Le Drian met with Prince Mohammed bin Salman, the Saudi crown prince, and Adel Al Jubeir, the foreign minister, in Jeddah on Saturday.
"If Tillerson can convincingly frame his mission as delivering a deal for the United States that is all about defeating terrorism... then he may have some chance", said Partrick, who focuses on Gulf politics.
The region's royal families detest the sort of critical scrutiny that is the stock in trade of news organizations like Al-Jazeera, and fear the anti-monarchical populism of groups like the Muslim Brotherhood.
While President Donald Trump welcomed the Arab states' decision to sever air and land links to their gas-rich neighbour, the State Department has taken a more neutral position and Tillerson has sought to broker a diplomatic solution.
Tillerson, the former chief executive of energy giant Exxon Mobil, arrives in the Gulf after a stop in Istanbul, where he discussed the Syria war to a failed 2016 coup in Turkey.
The statements caused a diplomatic crisis in the region when the UAE, along with Saudi Arabia, Egypt and Bahrain said the country supported terrorism.
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