The leaders of the opposition parties in the Welsh assembly have sent a joint letter to First Minister Rhodri Morgan calling for a meeting over top-up fees.
Labour were defeated in a vote on student top-up fees
It follows Tuesday's defeat of the Welsh Assembly Government when opposition AMs voted against any introduction of top-up fees in Wales.
The introduction of fees has been ruled out in Wales until 2007.
But the assembly government is due to consider a report on student funding in Wales, which is published on Thursday.
Assembly Members - including independent former Labour AM Peter Law - voted by 30 to 29 to rule out the introduction of university top-up fees in Wales in Cardiff Bay on Tuesday.
'Will of assembly'
On Wednesday, Plaid Cymru's Ieuan Wyn Jones, Nick Bourne of the Conservatives and Liberal Democrat Mike German wrote to Mr Morgan to call for a meeting to discuss the outcome of the vote.
The letter said: "Dear Rhodri, we are writing following yesterday's vote rejecting student top up fees in Wales.
"The three of us are obviously ready to meet with you to discuss...the way of implementing the will of the National Assembly for Wales as expressed in this vote.
"We look forward to hearing from you."
Education Minister Jane Davidson set up the Rees Commission
Plaid's Mr Jones added: "We are prepared to talk to Rhodri Morgan to ensure that higher education institutions are properly funded and that the burden of increasing debt is lifted from students in Wales."
Mr Bourne said: "We are willing to meet him at the earliest possible opportunity to discuss how we can implement the policy supported by a majority of assembly members."
And Mike German said a solution had to be found quickly so universities and students could plan for the future with certainty.
On Thursday, the Labour assembly administration is due to consider the report of a commission set up to look at the issue of how Welsh universities are funded.
The commission, headed by Professor Teresa Rees, has assessed a number of different proposals for a fees system in Wales.
Professor Rees and Labour had criticised opposition AMs for holding the assembly debate on fees before the Rees report was published.
But opposition AMs said they had a right to debate the issue.
Education Minister Jane Davidson urged the other parties to consider the implications of the Rees report once it was published.
She said: "We will get the independent report, we will then put a proposition on the table to discuss with all other parties, and I am pleased that the parties have said the door is open for discussion."
"Let's together decide the best system of student support in Wales."
A variable top-up fee of up to £3,000 is to be introduced in England in 2006, but the Welsh Assembly Government pledged not to introduce variable fees during its current term which ends in 2007.