Scotland's deputy first minister Nicola Sturgeon has said she will never support bringing in tuition fees for Scottish university students.
The SNP politician said her party would "always protect free education because it is one of the most important things any government can ever protect".
Labour MP Jim Murphy told the BBC's independence referendum debate education policy was already devolved.
He said Scotland already had free higher education.
However, Mr Murphy could not say what his own party's position would be in the future.
The current Scottish policy of free tuition in higher education applies to students from Scotland and from most of the European Union.
But students from England, Wales and Northern Ireland do pay fees similar to those south of the border.
The Scottish government has proposed to continue the policy if voters back independence in the 18 September referendum, and Scotland and the rest of the UK become separate EU member states.
Ms Sturgeon said: "I don't want to charge anyone for education wherever they come from but we have to do that now, and we will have to continue to do it, because Westminster has imposed sky high tuition fees in the rest of the UK."
She said the policy was necessary to prevent students from the rest of the UK depriving Scottish students of places at universities in Scotland.
Concerns have been raised that charging fees to students from the rest of the UK would be "incompatible" with EU law.
The deputy first minister said the Scottish government intended to raise an "objective justification" with the EU to continue the current charging regime.
Ms Sturgeon said she was "passionate" about free education, which was a "privilege" she had herself enjoyed.
She said: "I feel so strongly that having had that privilege, as a politician now and able to sit here partly because of that free education, I have got no right to pull that ladder of opportunity up behind me.
"I'll never be part of anything in politics that takes that away."
Mr Murphy, who has been campaigning with Better Together for a No vote in the referendum, said education policy was already devolved to Scotland.
He said: "We have devolution already. We can have free tuition fees here in Scotland already. The best of both worlds. A strong Scottish parliament with more powers coming without having to leave the United Kingdom."
When asked by the audience if he could promise free education, the Labour MP for East Renfrewshire said: "Each of the political parties will say at the next Scottish election what their priorities will be.
"Our party will set out its manifesto at the next election. This is much more important than one manifesto or one election."
Former Scottish Conservative leader Annabel Goldie said: "I know that within academia there is concern about the viability of our continued funding of higher education.
"So Nicola brays about Jim not having a policy, but these are devolved issues. This is nothing to do with constitutional change.
"University education is devolved. When we have a Scottish Parliament election you can look at the slate of policies, make your own mind up and vote for the policy you want."
Elsewhere in the debate, Mr Murphy said: "What we are told by the Scottish National Party and the Yes campaign is vote for independence and everything will be free. The fact is they are also saying taxes will be lower because corporation tax will be lower.
"You cannot build a socialist utopia in an independent Scotland on tax rates lower than George Osborne would even promise in a Tory Britain.
"It is unachievable because the figures don't add up in any way whatsoever."