The Russell Group of 24 leading UK universities argues that growing global competition will put the nation's reputation as a higher education powerhouse at risk unless funding is more targeted.
However, the appeal is controversial because student leaders and lecturing unions in Scotland have already warned that further concentration of research funding will result in a two-tier system.
Ferdinand von Prondzynski, principal of Robert Gordon University, in Aberdeen, also said the move could undermine the Government's wider economic strategy.
The Russell Group report, entitled Jewels in the Crown, says China has committed £7.2 billion towards achieving world-class status for 100 of its 3000 universities, while South Korea is investing £1.3bn to achieve 10 globally-recognised institutions.
In Germany, more than £2bn will be invested by 2017 in an initiative to create nine world- leading universities, while the US will double funding for key basic research agencies.
The report concludes: "It is essential that research funding is further concentrated to support world-class universities. Funding needs to be focused on rewarding truly world-class excellence on a grand scale and in high volumes."
Dr Wendy Piatt, director- general of the Russell Group, added: "Our international competitors are pumping billions of pounds into research and higher education and our leading universities are already under-resourced in comparison. There is a real danger that overseas universities will not only equal us, but will overtake us."
The Scottish Government has already moved to concentrate research funding on world-leading and internationally excellent research.
As a result, the Scottish Funding Council no longer funds lower-graded research and concentrates instead on work that ranks highest in international comparisons.
In 2012/13, newer universities such as Abertay in Dundee, Edinburgh Napier, Glasgow Caledonian, Queen Margaret in Edinburgh, and Robert Gordon will all see a cut to their share of Scotland's research budget – an annual fund of £233 million.
At the same time, research investment at traditional universities such as Glasgow, Edinburgh and St Andrews will increase, in some cases by as much as 6%.
Professor Nigel Seaton, principal of Abertay University, said: "Research funding is already heavily concentrated in the UK.
"It is not clear that further concentration would have a major impact on the UK's research performance, but it is clear that it would harm the learning experience of most students, whose opportunities to learn from active researchers would be reduced.
"Students at all universities, and from all backgrounds, benefit from a connection to the generation of new knowledge."
Robin Parker, president of NUS Scotland, said: "In Scotland, we're already seeing some moves to concentrate research at fewer institutions, and usually at the oldest and most elitist institutions too.
"Any moves to further concentrate research could threaten our sector as a whole, and mean that fewer and fewer students have access to the researchers and lecturers undertaking cutting-edge research."
Gordon Watson, president of UCU Scotland, said the Russell Group was correct to point out the danger of falling behind, but he said a wide variety of research, free from political interference, should be supported.