New visa rules restricting the number of foreign students able to come into the UK will seriously affect universities by putting off genuine students, university heads have told the Prime Minister.

David Cameron has been told in a letter circulated by Universities UK to take university students out of the net migration figures but the immigration minister Damian Green said such students are not visitors so need to be included.

The coalition is keen to stop foreign graduates from staying in the UK if they don’t get a skilled job paying £20,000 or more. They would also not be able to study for further qualifications for more than five years.

The letter – signed by 68 chancellors, governors and university presidents, as well as Greg Dyke, Lord Melvyn Bragg and Sir Menzies Campbell – claimed that foreign university students bring close to £8bn a year into the UK and this could double in the next 13 years.

“In this Olympic year, when our universities will be hosting athletics teams and media from across the globe, we urge you to send a clear message that genuine international students are also welcome in, and valued by, the United Kingdom,” the letter said.

It went on: “Global competition for international students is intense and a number of other countries are increasing their efforts in this area. 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.

“We believe this would help government by creating a clear differentiation between temporary and permanent migration, help universities whose international character is essential to their future success, and help the UK by contributing to economic growth.”

But Green said: “Public confidence in statistics will not be enhanced by revising the way the net migration numbers are presented by removing students.”