The Federal Institutes of Technology, including the schools in Zurich and Lausanne, have asked for additional funds to keep up with their competitors abroad.
The board said an increase in the annual budget of at least six per cent was needed for academic training and research over the next five years.
The six institutions, two schools and four application-oriented research organisations, currently receive a total of SFr2 billion ($2 billion) from the government.
The funds available were no longer sufficient to meet the demand of a growing number of students in recent years, board members told a news conference in Bern on Thursday.
They warned it might be necessary to limit the numbers to maintain high quality standards.
Extra finances were also key to launch and continue research projects, notably in robotic and computer science as well as nanotechnology.
swissinfo.ch and agencies