Speaking after talks with President Emil Constantinescu, Mr Rifkind said that Western governments had been impressed with the direction Romania was taking both in terms of its economy and improved relations with neighbouring countries.
"For Britain, as for other Nato countries, the events of the last few months have been important," said Mr Rifkind, the most senior Western politician to visit Romania since the elections. "They have demonstrated the strength of Romania's democratic institutions ... and they have certainly helped Romania's case with regard to Nato."
Mr Rifkind's words were music to the ears of his hosts, who have long had membership of Nato as their number one foreign policy goal. They also came barely a week after France went considerably further by publicly throwing its weight behind Bucharest's bid to join the alliance.
Romania's foreign minister, Adrian Severin, praised what he described as Britain's "open, pragmatic stance" on the Nato expansion issue and said he hoped the alliance would open its doors simultaneously "to all countries belonging to the same geo-strategic region".
Although no formal decisions have yet been taken, Nato leaders meeting in Madrid in July are expected to name Poland, Hungary and the Czech Republic as the first former Communist Bloc countries to be invited to join the organisation, probably in 1999. Romania and the former Yugoslav republic of Slovenia are considered the next strongest contenders.
The Czech Republic is one of the front-runners to join an enlarged Nato, the secretary of State for Defence, Michael Portillo said on Tuesday. Mr Portillo met the Czech Defence Minister Miloslav Vyborny in London to sign a memorandum of understanding between the two countries to deepen military ties.