Fianna Fáil says it is insisting in talks with the Government that next week's budget should set aside up to €100 million for higher education to help tackle a "funding crisis".
It also says it wants a reduction in the pupil-teacher ratio at primary level at school which is a condition of its support for the Government under its confidence-and-supply agreement.
Thomas Byrne TD, Fianna Fáil's education spokesman, said higher education needed significantly more funding following years of cuts.
The Cassells report on the future funding of higher education said that €100 million a year in extra funding was needed if the State was to build a world-class system.
Last year, the Government allocated an additional €36 million which Mr Byrne said was nowhere near enough to rebuild a sector which suffered more than any other part of the education system during the downturn.
If the Government was serious about third level, it needed to match this ambition with adequate resources, he said.
Mr Byrne's call echoes a pre-budget submission of the Irish Universities Association, which says a rapid increase in resources is needed to protect quality and address capacity constraints in the sector.
It says colleges will not be able to accommodate an projected increase in enrolment of up to 30 per cent over the next decade unless the sector is funded properly.
Priority
A spokeswoman for Minister for Education Richard Bruton said higher education was a central part of the Government's plan to support a strong economy and deliver a fair society.
The package of measures the Government announced for the sector in the budget for this year reflects this priority.
She said this year’s additional investment was the first significant increase in nine years and formed part of a €160 million investment over a three-year period.
In addition, she said plans for a new “employer-exchequer mechanism”, which had the potential to increase employers’ contribution to higher education by €200 million a year by 2020, were under consideration.
On the issue of the Cassells report, she said it was being examined by the Oireachtas education committee.
“Examining the proposals in this report is key to putting in place a sustainable system of funding that can deliver a world-class third-level system for the medium and long term,” she said.
“This is an area where broad political consensus is needed on the future direction and Minister Bruton will be working to build that consensus.”
Separately, the Government will launch a new “international academic mobility programme” on Monday to fund collaborative activity between Irish universities and global institutions.
A fund of €500,000 has been dedicated to the programme, giving an estimated 100-150 academics from universities, institutes of technology and colleges in Ireland the opportunity to travel to and collaborate with key strategic partner institutions across the world.
The fund is open to teaching, technical, management and administrative personnel from eligible institutions to apply to the programme.
The Higher Education Authority is to run an open, competitive call for proposals with a view to making awards by the end of 2017.
Mr Bruton said links with other countries were even more important in light of the UK's decision to leave the European Union.
Irish universities have extensive research links with UK colleges, and many of these relationships will be in doubt depending on what relationship Britain forges with the EU.
“Working closely with international institutions is key to the success of our higher education sector, especially in light of Brexit, and the other global challenges and uncertainties we face,” he said,
“This programme will be in addition to supports already available under the Erasmus+ initiative that facilitate, for example, student exchange and partnerships between higher education institutions”.
Minister of State for higher education Mary Mitchell O’Connor said it formed part of a wider strategy of increasing the number of international students coming to Ireland to study.