France retreated from threats to clog up exports and ban UK fishers from landing catches on its coast because it “looked more closely at the evidence”, the environment secretary, George Eustice, has said.

Eustice denied the UK had acted in any way improperly and said it continued to abide by its obligations. France has been infuriated that some of its small boats are being denied permission to fish in waters around the UK and Channel Islands.

The UK insists its licensing regime is reasonable and it will continue to require boats to provide evidence that they have previously fished in those waters on at least four days in the past four years.

“As far as we’re concerned, we had an agreement. We’ve been implementing it in good faith. We’ve issued licenses to everyone that is entitled to one,” Eustice said.

“We made clear last week that we thought the threats that France made were disproportionate. We felt they were very disappointing because we’ve been implementing the agreement.

“We just very much welcome the fact that France has stepped back from that course of action. And of course we continue to have dialogue if there are additional vessels that qualify,” he told BBC Radio 4’s Today programme.

On Monday night, the French president, Emmanuel Macron, stepped back from the retaliation he had said he would impose on the vital goods artery from midnight because of a dispute over access for its fishers to British waters.

The cabinet minister Lord Frost is to meet Clement Beaune, the French minister for European affairs, in Paris on Thursday, to renew talks on the row over licenses granted to French fishers.

Eustice said the UK government wanted to see the heat taken out of the talks. “We very much welcome the fact that France has stepped back from the threats that they made last Wednesday. This whole situation has been de-escalated and there will be further discussions on Thursday,” he said.

Almost 1,700 EU vessels have been licensed to fish in UK waters, equating to 98% of EU applications for fishing licences, the UK government says, but this figure is disputed in Paris. The main area of disagreement is over the number of small French vessels given access to the immediate coastal waters of the UK and Jersey.

On Tuesday, Bruno Bornell, an MP for Macron’s La Republique En Marche party, said Johnson was “bluffing” and that the dispute was an ongoing “scallop war”. He said more than 40% of French requests for licenses had been delayed by up to 10 months – and that French boats were being subject to more checks than other countries such as the Netherlands or Belgium.

“Fishermen are the tip of the iceberg,” he told Today. “We’ll see discussions like this all along if nobody wants to play fair. And that’s exactly the situation we’re in now. What we’re asking for is respect, to respect the Brexit treaty. Nothing else, nothing more.”