Haibatullah Akhundzada has been the spiritual chief of the movement since 2016 but has remained a reclusive figure, even after his group seized power in Afghanistan in August.
The US president said that some soldiers could remain past the August 31 deadline to ensure all Americans get out.
The country will be governed by ruling council that would be answerable to the supreme leader Haibatullah Akhundzada.
The visit has stirred speculation that peace talks between Pakistan and Afghanistan Taliban may be revived.
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