The letter has been signed by almost 70 business leaders, peers from all major parties and other prominent figures.
The signatories include writer and broadcaster Lord Bragg, who is chancellor of the University of Leeds, former director-general of the Confederation of British Industry, Sir Richard Lambert, who is chancellor of the University of Warwick, and actor Sir Patrick Stewart, chancellor of the University of Huddersfield.
The letter says recent government measures to tackle the abuse of the student visa system were “welcome” but it urges David Cameron to “support our universities in their efforts to recruit genuine international students”.
It follows concerns universities are being harmed by the tougher visa rules, which critics claim have made UK institutions a less attractive destination for overseas applicants.
“Global competition for international students is intense and a number of other countries are increasing their efforts in this area,” the letter states.
“We therefore ask you to consider how your government can do more to support our universities in their international activities.
“In particular we request that international university students be removed from the net migration statistics for policy purposes, bringing us into line with our major competitors.”
The call comes after the latest statistics showed the government is struggling to make progress against its target of cutting net migration by tens of thousands during the course of the current Parliament.
University vice-chancellors argue that students should not form part of the net migration count because the vast majority are temporary migrants who return to their country of origin on completing their studies.
• See Times Higher Education tomorrow for the results of an exclusive survey on the latest state of applications to universities from international students.