Mr Rifkind's trip was planned before last week's bomb attack in Dhahran which killed 19 US servicemen. But it gave the Foreign Secretary the chance to brief Saudi officials on the decision by leaders of the world's top industrialised nations at the G7 summit in Lyons to boost the fight against terrorism.
Britain has been keen to end the row over Mr Masari, a fundamentalist Islamic dissident who has bitterly criticised the Saudi royal family since fleeing to London in 1995.
British businessmen had warned that his attacks could threaten trade with Saudi Arabia. The Foreign Office had tried to deport him, but was blocked by a British court.
Mr Rifkind told a news conference after talks with Crown Prince Abdullah and Foreign Minister, Prince Saud al-Faisal, that the matter had not affected relations between Riyadh and London.
"The subject of Mr Masari has only been raised once, very briefly, and only to dismiss it. It is clearly agreed that it is irrelevant to our relations."
To emphasise the British Government's anger with Mr Masari, Mr Rifkind briefed Saudi officials on a British plan to change the United Nations convention on refugees to stop people taking advantage of asylum laws while promoting, funding or assisting terrorism.
The plan would not affect Mr Masari, but could prevent "future Masaris'', said an aide. Saudi officials have been angered by his recent remarks, in which he supported what he called the intellectual arguments behind the Dharan bombing, although he denied involvement.Reuse content