The Government would back “sustainable increases” in the number of international students at British universities, the Chancellor has said.

Ministers have come under pressure to cut international student numbers as part of a wider effort to reduce net immigration to the UK, but university leaders have warned that such a move would be “calamitous” for the sector.

The Government has already sought to cut numbers by placing new restrictions on the ability of foreign students to bring family members with them.

But on Friday, Jeremy Hunt suggested the Government would welcome some increase in international student numbers, provided it was driven by a desire for education and not immigration.

He told reporters: “We have rightly introduced some changes that ensure that people are coming to this country because they want to study as some of the brightest and best from around the world, not as a vehicle which is primarily to bring their families over and to settle in the UK, which is not the point of the exercise.

“I think we will see some reductions in migration flows as a result of those decisions being taken, but that does not mean that we won’t continue to support sustainable increases in international students coming to the UK.”

His comments follow calls from some Conservative MPs for further cuts to international student numbers, including by scrapping the graduate visa.

The visa, which allows foreign students to live and work in the UK for up to two years after graduating, is seen by some MPs as a backdoor for longer-term immigration to Britain.

On Tuesday, the Migration Advisory Committee found no evidence of widespread abuse of the graduate visa route and warned some courses would become “less financially viable” if the number of international students was cut.

Downing Street said the Government would respond to the report “in due course”, but added it was working to reduce migration levels.

The Prime Minister’s official spokesman said: “(The Prime Minister) has said before that British students should be the priority for our education system and universities and student visas must be used for education, not immigration.”

Universities reported earlier this week that applications from international students had already fallen by a quarter following the new restrictions.

Dame Sally Mapstone, president of Universities UK, said further restrictions were “unnecessary” and would be “calamitous not just for institutions, but actually for the UK as a whole”.