The culture minister has visited the British Museum in London in an attempt to have the historic Lewis chessmen returned to Scotland.
Ms Fabiani met the British Museum deputy director Andrew Burnett
The 13th Century figures were found on a beach on the Isle of Lewis in about 1830 and most are kept at the museum.
Linda Fabiani asked the museum's deputy director to consider their return.
The British Museum said the figures probably originated from Norway and had frequently been loaned to museums in Scotland.
On her visit, Ms Fabiani viewed the chessmen, which are on permanent display at the museum.
She later met Andrew Burnett, the museum's deputy director, who told her the artefacts were an important symbol of European civilisation.
A statement issued by the museum after the meeting said: "Each year millions of visitors, free of charge, admire the chessmen at the British Museum and they are frequently loaned for display to museums in Scotland, across the rest of the UK, and around the world."
It outlined 27 loans of the pieces which had been agreed in the past 10 years.
"Both parties agreed that discussions should continue about exhibiting the chessmen to maximise public benefit," the statement added.
A total of 11 of the artefacts are kept in Scotland
The museum said the chessmen were probably made in Norway, between about 1150-1200 AD.
During this period, the Western Isles - where the figures were buried - were part of the Kingdom of Norway, not Scotland.
The figures of seated kings and queens, with bishops wearing mitres on their heads and knights mounted on horses, include two complete sets and pieces from two or three others.
They were discovered by a shepherd in a small stone chamber 15ft beneath a sand bank on a beach near Uig.
Ms Fabiani told the Scottish Parliament earlier this week it was "unacceptable" that 82 of the 93 chessmen were based in London.
Only 11 of the artefacts are housed at the national museum in Edinburgh.
After her visit to the museum, the minister said: "The government will continue to consult with interested parties to reach a consensus in Scotland and we will then take matters forward with a proposal."
The Western Isles MP, Angus MacNeil, is preparing a bill which would allow the pieces to return north by giving the British Museum the freedom to give away or sell parts of its collection.
But the Scottish Government's position came under fire from Labour this week, when culture spokesman Malcolm Chisholm questioned whether the chessmen campaign would mean that Napoleonic artefacts based in Scotland would now be repatriated.