Oman TV showed a gaunt but visibly animated Qaboos greeting the foreign secretary, accompanied by his minister responsible for foreign affairs, Yusuf bin Alawi.
Qaboos, the longest-serving ruler in the Arab world, keeps a low profile on regional disputes, carving a niche for Oman as a diplomatic backchannel, notably between the West and Iran.
Johnson landed in Muscat at the start of a three-day tour that will also cover Iran and the United Arab Emirates.
He will also press for the release of dual national Nazanin Zaghari-Ratcliffe, who was sentenced to five years in prison in September 2016 for taking part in mass anti-regime protests in 2009 -- a charge she denies.
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She is due to face fresh propaganda charges in court on Sunday, which could land her several more years in jail.
The case has become highly politicised, especially after a "slip of the tongue" by Johnson last month when he stated that Zaghari-Ratcliffe had been training journalists in Iran, which has been used by the Iranian authorities to help justify the new charges.
Iran state television aired a new video about Zaghari- Ratcliffe today, accusing her of taking part in covert activities against the country financed by Britain and the United States.
Tehran does not recognise dual nationalities, and it has refused access to her for representatives of the British authorities, making a prison visit for Johnson unlikely.
Zaghari-Ratcliffe's husband Richard Ratcliffe has said Johnson's visit to Iran is likely to give his wife hope.
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