UK immigration minister James Brokenshire has refused to commit to allowing Scotland to develop its own scheme to make it easier for graduates from non-EU countries to stay and work in the country.

In a letter to Holyrood committee, the junior Home Office minister said "the case needs to be argued" for any changes and claimed that current UK-wide visa schemes for international students amounted to an "excellent" offer.

Mr Brokenshire's position clashes with expert evidence heard at the Scottish Parliament last week, when it was claimed a 2012 decision to revoke an automatic 24 month post graduation visa for international students meant universities were struggling to compete with other nations and the country was suffering a "brain drain" of talent.

There is a growing clamour for Scotland to be allowed to bring in its own initiative which advocates claim would boost universities, colleges, the economy and wider society. The move is backed by all Holyrood parties, including the Scottish Tories, and businesses.

However, Mr Brokenshire appeared to downplay the chances of the Home Office sanctioning a radical alternative north of the border.

In response to the Scottish Parliament's devolution committee, he said the previous post-study work visa was open to abuse and undermined migration policies.

He added: "Despite the convincing evidence in support of the current scheme I recognise that it is important that such schemes are kept under review; to ensure that they continue to deliver for all parts of the UK.

"If there are different views as to how best to make this work, then the case needs to be argued. I welcome the current inquiry by the Scottish Affairs Committee and the separate initiative established by the Scottish Government minister for Europe and International Development and I shall look carefully at the reports of both and any recommendations made to improve further the current scheme."

Currently, students face being kicked out of the country if they do not secure graduate level employment paying at least £20,800 within four months of graduating, a situation many argue is putting international students off applying in the UK.

Bruce Crawford, convener of the devolution committee, said there was a growing consensus from colleges and UK universities that the current schemes on offer were "far from excellent".

He added: "Evidence we've heard directly from universities and colleges in Scotland indicates the brain drain effect is already impacting negatively on the UK as a study destination and businesses are being deprived of a world-class pool of talent, trained and developed in Scotland.

"The Home Office says the case for a new scheme needs to be argued, that's precisely the issue we will be considering when we produce a report shortly."