In a speech broadcast on the Doha-based satellite channel Al-Jazeera in the early hours, Foreign Minister Sheikh Mohammed bin Abdulrahman Al-Thani also called for "a dialogue of openness and honesty" to resolve the crisis.
Saudi Arabia, the UAE, Bahrain, Egypt, Yemen and the Maldives severed ties with Qatar yesterday over accusations it supported extremism.
Qatar has denied the allegations, in the biggest diplomatic crisis to have hit the region in years.
The minister said Qatar's ties to the US were complicated, but would remain unharmed.
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"Our relationship with the United States is strategic," said Abdul Rahman. "There are things we do not agree on, but our areas of cooperation outnumber those of contention." He did not elaborate.
Qatar hosts the largest US airbase in the region, which is crucial in the fight against Islamic State group jihadists, and is set to host the 2022 football World Cup.
It also follows weeks of rising tensions between Doha and its neighbours, including Qatari accusations of a concerted media campaign against the kingdom and the alleged hacking of its official news agency.
Kuwait, like Saudi and Qatar a powerful member of the Gulf Cooperation Council, has remained noticeably silent on the crisis.
Abdul Rahman said Kuwaiti ruler Sheikh Sabah had specifically requested Qatari Emir Sheikh Tamim bin Hamad Al- Thani postpone a planned speech today in a bid to contain the crisis.
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