The crisis was triggered by last month's cutoff of diplomatic relations between Qatar and Arab countries, who accuse Doha of supporting terrorism.
Mogherini is scheduled to meet senior Kuwaiti officials to show support for Kuwaiti mediation to solve the crisis, according to the official KUNA news agency.
Saudi Arabia, Egypt, the United Arab Emirates and Bahrain have imposed a land, sea and air blockade on Qatar and presented a list of demands to Doha to end the siege, including the closure of the Al Jazeera television network and Turkish base in Doha, or face further sanctions.
Doha denies the accusation of terrorism and contends the blockade is a violation of international law.
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