The Home Office minister said it was “essential” to shift the perception, after recent rule changes, that the doors were closed to non-EU students.
“Please come, we have got some of the world’s best universities,” he said.
Mr Green is under pressure from business and university chiefs to relax visa restrictions.
They want foreign students to be exempted from the government’s target of reducing net migration from its current level of about 250,000 a year to “tens of thousands” by 2015.
But MPs on the Commons business select committee were told it was too early to say with certainty that the government’s policy had significantly damaged UK universities.
And it was often the perception that Britain was now tough on immigration – rather than the reality of its actual policies – that was acting as a deterrent to elite foreign students.
Simon Walker, director general of the Institute for Directors, said: “Remarks that are made in Westminster, or around the country, that go do down quite well locally are often on the front page of The Times of India and the New Straits Times the next day, because of the internet, and the impacts on this on perceptions of Britain are quite strong.”
Nicola Dandridge, chief executive of UK Universities, said she could “live with” with any one of the government’s immigration policies taken in isolation even if some, such as a minimum salary of £20,000 for post-study work visas, appeared overly tough to some potential undergraduate or graduate students.
But, she argued, it was the “aggregate” of the changes and the way they had been implemented that was in danger of putting Britain at a disadvantage to its major higher education competitors such as the US, Canada, Australia and New Zealand.
“We are viewed as being at the more stringent end of the spectrum and that’s a question of substance as well as perception,” she told MPs.
She said there had been a 10% increase in applications from non-EU students to British universities this year but future projections and “anecdotal” evidence from recruitment fairs suggested the rate of increase would slow.
“The 10% increase, or whatever it may be, is of course positive and it’s wholly welcome but that’s against the background of us having had a very dominant and wonderfully successful market position and we are slipping.
“The international student market is growing and we want to be part of that.”
She said a lot of the increase had come from Chinese students “which is completely wonderful” but they tended to study business and management and there were signs that students from Brazil and India, who tended to study scientific and technical subjects, were increasingly choosing countries that appeared more welcoming.
“We cannot say it’s only the government’s policies but the atmospherics, the way this is playing internationally, which is, I think, causing real problems,” she added.
Mr Green insisted that Britain’s universities would not be harmed by the government’s visa restrictions, which he said were mainly aimed at closing down bogus colleges and preventing students without a job from staying in the country and claiming benefits after they had finished their course.
But he also appeared to concede that the government’s anti-immigration rhetoric was going down badly in Britain’s target higher education markets.
Asked how much work was being done by the government to change the perception that the UK had turned against foreign students, he said: “A lot.”
“And it’s slightly swimming against the tide because, if the thought is out there that we have changed the system to make it more unfriendly, then reversing that perception is important and difficult but very, very essential.
“We have changed the system to cut out the abuse, we have changed the system to skew it towards the best students, skew it towards universities.
“But doing that at the same time as cutting out abuse is a nuanced message to send out.”
He said now that the changes were in place “I think the sensible thing to do is to let the system bed down while we relentlessly go round the world saying the brightest students and the best are as welcome as ever to Britain”.
BBC © 2012