Not a single UK university meets all the requirements for being a truly international institution, according to the vice-chancellor of the University of Bristol.
Speaking at the Going Global conference, Eric Thomas gave a list of criteria he believed were crucial to a global university, beginning with "brand promotion" in major disciplines.
Also on the list were "excellence throughout" - including finances, administration, governance and leadership - and an undergraduate curriculum "structured to prepare its students for the global world".
The transnational institution must be involved in major research projects "addressing knowledge issues that are facing society", such as climate change, Professor Thomas said, and must draw its students and academic staff from all over the world.
Staff should be "addressing global institutions" such as the World Health Organization, the World Bank and the United Nations, as well as working with global companies.
At the session "What makes a truly global university?", Professor Thomas said that "not one" UK university was fulfilling all the criteria.
John Sexton, president of New York University, talked about "diversity of mission" between different types of universities.
He said that institutions should develop internationalisation strategies depending on "where in the world educational profile you sit", with the research university and the community college being "different parts of the same world".
Timothy Tong, president of the Hong Kong Polytechnic University, said a key challenge for international universities was the balance between overseas and domestic students.
"For example, I have experience of teaching in public universities when the international student population reached a critical point," he said.
He added: "Local lawmakers may question, 'Why are we spending local taxpayers' money to educate so many students who are not from the local community?'"