Scottish Education Secretary Michael Russell made the call in his letter to the Scottish Funding Council setting out priorities for the sector for 2015/16.
The Government has already created extra places for widening access to ensure other talented students do not miss out.
Mr Russell said the additional funded places would not be expanded further, but would be maintained at current levels.
But he added: "These additional places must act as a catalyst for further action by universities to ... opening their doors to a student body that is representative of all of Scotland's communities."
A Universities Scotland spokesman said: "We are engaged with the SFC over widening access that gives a proper account of the diversity of the student population."