Liam Fox says that staying in a permanent customs arrangement with the EU would “not be delivering Brexit”.
The international trade secretary said he did not believe the UK could have an independent trade policy if it stayed in a customs union.
The PM and cabinet ministers discussed “next steps” at No 10 on Friday, after her Brexit plan was defeated by MPs.
Labour says the Tories are so divided they cannot get an agreement that can bring people together.
Some opposition parties have been making the case for a customs union. Theresa May held talks with the leaders of parties including the SNP and the Lib Dems, about a way forward after she won a confidence vote by a narrow margin in the Commons on Wednesday.
She also spoke to German Chancellor Angela Merkel and Dutch Prime Minister Mark Rutte on the telephone on Thursday night, and will be speaking to more EU leaders over the weekend.
But Labour Leader Jeremy Corbyn, who wants the UK to be in a permanent customs union with “strong” ties to the single market, has refused to take part in talks with the prime minister until she rules out the prospect of leaving the EU without a deal.
As many as 20 Tory ministers have also said they would quit the government unless the prime minister allows them to try to stop a no deal Brexit, according to the Telegraph.
Mrs May says ruling out no deal is impossible as it is not within the government’s power.
The UK is due to leave the EU on 29 March, under the Article 50 process and the UK’s EU Withdrawal Act, with or without a deal – unless the UK chooses to revoke Article 50 and continues as a member of the EU.
Mr Fox, who backed Leave during the referendum campaign, said that people expected the government to honour its commitment to leave the customs union and single market, as set out in last year’s Conservative Party manifesto.
By staying in a customs union, the UK would “have to apply European trade law without having a say in how it’s made” and apply a common external tariff, which would “restrict our ability to make agreements outside the European Union’s ability to do so,” he added.
Mr Fox also backed Mrs May’s conclusion that the government could not rule out a no-deal Brexit.
Separately, he conceded that no post-Brexit trade deals have been confirmed, saying they depended on whether other countries were willing to “put in the work”.
The Department for International Trade said some deals are at an advanced stage, but none have been rolled over so that they will cover the UK post-Brexit.
The BBC’s business correspondent, Jonty Bloom, said the closest the UK has come is an initial agreement with Switzerland to replicate the existing EU-Switzerland arrangement “as far as possible”.
But he said that deal has not been formally signed yet and the details of what “as far as possible” means are not clear.
In 2017, Mr Fox predicted that the UK could “replicate the 40 free trade agreements” the EU has around the world before it left the bloc.
Writing in the Financial Times, Shadow Chancellor John McDonnell said: “The Tories are fundamentally unable to implement the referendum result in a way that brings the country together, and that is just exacerbating the frustrations and divisions that brought about Brexit. There is a warning here.
“Voters need to see Parliament taking decisive action, and soon. The alternative is yet another systemic failure, one that could provoke even greater disillusionment with our system.”
He said the Conservative Party was “riven with division” so Labour would “return to Parliament to promote the compromise we believe is not only in the best interests of our economy but is also capable of securing sufficient support both here and in Brussels”.
If Parliament was at an impasse, and Labour could not get a general election “we should also retain the option of seeking a public vote,” he added.
Mr Corbyn has come under pressure from dozens of his MPs to back calls for another EU referendum. On Friday a pro-referendum campaign group paid for a wrap-around advertisement in his local newspaper, the Islington Tribune , urging him to back a “public vote on Brexit”.
Meanwhile, former Labour prime minister Gordon Brown urged the government to extend Article 50 by a year. But former foreign secretary Boris Johnson said changing the date of leaving from 29 March would be “shameful”, and the public would view it as “an elite conspiracy to thwart Brexit”.
Giving a speech at JCB Headquarters in Rocester, Staffordshire, he instead urged the government to use Brexit to “unite the country”.