US First Lady Michelle Obama has flouted an ultra-conservative Muslim kingdom’s strict dress code during a recent political visit.

Mrs Obama touched down in Saudi Arabia on Tuesday with her head uncovered, which would be a breach of Sharia Law for a local woman.

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The First Lady was accompanying her husband President Barack Obama, who landed in the Saudi capital of Riyadh for talks with new King Salman following the death of King Abdullah.

A throng of Saudi men greeted the Obamas, with not a woman in sight. Photo: AAP

Saudi women are required by religious law to dress head-to-toe in black, but Mrs Obama chose to wear dark slacks, a blue top and no headscarf.

Some of the male Saudi officials who welcomed the Obamas to the capital refused to shake the first lady’s hand.

The Muslim kingdom abides by a strict form of Islamic law known as Wahhabiism, and imposes many of the same harsh penalties, including beheadings and hand amputations, as the terrorist organisation Islamic State.

Head coverings are not required for foreigners, but local women are banned from driving and must receive the permission of a male relative to travel, marry and study at university.

Saudi Arabia is a close strategic ally of the US. King Salman, 79, acceded to the throne after Abdullah died on Friday aged about 90.

– with AAP