Justice Secretary Michael Gove has challenged David Cameron's claim his renegotiation deal with EU leaders over the UK's membership is legally binding.
Mr Gove, one of five cabinet ministers calling for the UK to quit the EU, told the BBC the European Court of Justice could throw out some of the changes.
But attorney general Jeremy Wright said the deal was "irreversible".
He said that was not only his opinion, but also the view of the government's lawyers and European lawyers.
And Downing Street cited a former director of legal services at the EU, Alan Dashwood, who said the "Decision" was a binding legal agreement reached by consensus and could only be amended or rescinded by consensus - or, "in other words, with the agreement of the UK".
"So, in that sense, it is irreversible," he said.
In an interview with the BBC's political editor Laura Kuenssberg, his first since he opted to oppose Mr Cameron in the referendum, Mr Gove also said:
- His "deep feelings" on the issue outweighed his friendship with the prime minister when deciding which way to campaign
- Leaving the EU would enable the UK to control the "type" of migrants who entered the country
- EU rules are constraining the UK's ability to make key decisions on infrastructure
- He did not urge Boris Johnson to back EU exit during a dinner last week
A UK referendum on whether to remain a member of the EU will take place on 23 June.
The reform deal paving the way for the referendum promises changes to the EU's binding treaties in two areas - exemption for the UK from an "ever-closer union" and protection for countries not using the euro - although it does not specify when this will happen.
Mr Gove said that without Treaty change all elements of the PM's renegotiation settlement were potentially subject to legal challenge.
"The facts are that the European Court of Justice is not bound by this agreement until treaties are changed and we don't know when that will be," he said.
He said Mr Cameron was "absolutely right that this is a deal between 28 nations all of whom believe it", adding: "But the whole point about the European Court of Justice is that it stands above the nation states."
Mr Cameron has "not been misleading anyone", Mr Gove went on, but he added: "I do think it's important that people also realise that the European Court of Justice stands above every nation state, and ultimately it will decide on the basis of the treaties and this deal is not yet in the treaties."
By Clive Coleman, BBC legal affairs correspondent
Is Michael Gove correct that the prime minister's renegotiation deal is not legally binding? Lawyers will argue it both ways.
The deal is not a formally ratified treaty, but would still be regarded by many as legally binding in international law.
The Vienna Convention on the law of treaties makes it clear that states can express their consent to an international agreement in a variety of ways - signature, acceptance or approval.
What is important is the substance of the agreement and not the label "treaty". As Mr Gove acknowledges, this is a "deal between 28 nations all of whom believe it". In other words all of whom intend to be bound by it.
The more significant question is, perhaps, what is the value and status of the deal as a matter of EU law?
It is intended to be fully compatible with the existing EU treaties - all of the member states agree on that. However it is not an amendment to the existing treaties and remains subject to the interpretation of the European Court of Justice (ECJ).
That may make it sound weak and vulnerable to legal challenge. However, all measures of EU law under the existing treaties are subject to interpretation by the ECJ.
Should any state subsequently raise the issue of the relationship between the deal and the existing EU treaties, that would be a matter for the ECJ to rule upon.
So, while some legal experts acknowledge that a legal challenge is theoretically possible, the ECJ would give substantial weight to the fact that all 28 member states have agreed both the deal and that it is compatible with the existing treaties. That makes the chances of a successful legal challenge slim.
On Monday, Mr Cameron told MPs: "The reforms that we have secured will be legally binding in international law, and will be deposited as a treaty at the United Nations.
"They cannot be unpicked without the agreement of Britain and every other EU country."
The European Court of Justice (ECJ) was set up in the 1950s to ensure EU law is interpreted and applied evenly in every EU country but many Tory MPs believe it has over-extended its jurisdiction and its powers should be rolled back.
Martin Schulz, the president of the European Parliament, said the guarantee that the UK would be exempted from ever-closer union would be "written exactly" into the treaties in the form it was agreed last week and "nobody can tell British voters other things".
Analysis: 'Europe could throw out the changes'
By BBC political editor Laura Kuenssberg
Mr Gove's comments will be catnip for eurosceptics who've already been arguing that Mr Cameron's deal is hardly worth the paper its written on.
For David Cameron, maintaining the sense that the deal he's achieved can and will improve the UK's relationship with the rest of the European Union in a meaningful way is a vital part of his campaign.
It's one thing Tories from different parts, different generations of the party, disagreeing. It's quite another when it is two who have shared political hopes, ambition, and even family holidays.
Attorney general Jeremy Wright, the government's senior law officer, told the BBC that although challenges could be brought to the ECJ, the UK agreement had "very similar legal strength" to existing treaty obligations.
"The suggestion that this agreement does not have legal effect until it is incorporated into EU treaties is not correct. That is not just my opinion - it is the opinion of this government's lawyers, lawyers for the EU, and, I suspect, the majority of lawyers in this country."
And former attorney general Dominic Grieve told the BBC that Mr Gove was simply "wrong".
But the justice secretary's comments were seized upon by Conservative MPs campaigning for the UK to leave the EU.
Andrew Percy, the MP for Brigg and Goole, tweeted: "Increasingly clear the EU agreement has no force in law. Those arguing it does are having their argument undermined by EU politicians daily."
Ministers who want to quit the EU have been allowed special dispensation to oppose the government at the referendum, although strict rules have been put in place for the campaign.
In the BBC interview, Mr Gove rejected claims a vote to leave was risky, saying the EU was an "old-fashioned model" and departing would offer "a tremendous opportunity for Britain to recover its mojo".
"Optimists - people who believe in Britain, who believe in democracy - they're the people I believe who will vote for us to leave and take back control."
At the moment, he said the UK could not control overall levels of immigration or its composition and this needed to change.
"In my view our immigration policy means that we have some people who can come into this country who we might want to say no to and others, who we might want to attract, who can't currently come in.
"So it's not for me a matter of numbers, it's a matter of the type of people that we want in this country. That's why I think we need to leave, take back control and decide who we want in this country and at what rate."
Elsewhere in the EU referendum debate, 13 senior military officers have signed a letter to the Daily Telegraph saying being in the EU "helps us to safeguard our people, our prosperity and our way of life".
But UKIP defence spokesman Mike Hookem said it was "laughable" to say that the UK could not cooperate militarily with its allies unless it was part of a "political structure".