Writing in the FEFC's annual report, Professor Melville also called for a level playing field for all post-16 education.
His words come just days before Education Secretary David Blunkett addresses principals at the Association of Colleges' conference next week. Mr Blunkett has promised extra cash for colleges.
He said: "Without a stronger financial base, the council will find it increasingly difficult to ensure that there are sufficient and adequate facilities for further education. Colleges will find it difficult to meet the urgent challenges now facing them."
Professor Melville said it was "unfortunate that, at a time when the need and demand for FE is increasing, student numbers funded through the council may fall in the year ahead due to the reduction in the funds available".
Professor Melville welcomed developments such as the Government's Welfare to Work programme and the Dearing report on higher education, saying they would improve the position of FE. But he warned that the developments would not ease colleges' financial plight.
Professor Melville added: "It is unfortunate that, at a time when the need and demand for further education is increasing, student numbers funded through the council may fall in the year ahead due to this reduction in the funds available."
His comments were echoed by FEFC chairman, Sir Robert Gunn, also writing in the report. He said: "The council believes that the new administration must address urgently the weakening financial health of the college sector if reductions in essential provision in future years are to be avoided.
"A fair and secure funding base is also essential if institutions are to deliver successfully their part in the Government's education and social agenda."