Apple claims it does not know that the UK was working on a "hybrid" version of the NHS coronavirus contact monitoring app using technology developed with Google.
The firm took the unusual step of saying that it was also unaware of a problem related to distance measurement, which was reported by health secretary Matt Hancock in Thursday's daily briefing.
Apple said it was "difficult to understand" the claims.
Downing Street said the government "has worked closely with Apple and Google."
In tests carried out in the United Kingdom, there were occasions when the software tools developed by Apple and Google were unable to distinguish between a phone in the user's pocket 1 m away and a phone in the hand of a user at 3 m away.
During the briefing, Hancock said: "Measuring distance is clearly mission critical for any contact tracking app."
However, speaking to the Times, Apple said: "It is difficult to understand what these statements are since they have not spoken to us."
The company also pointed out that the technology was already in use or intended for use in Germany, Italy, the Netherlands and Ireland.
The tech giant also expressed surprise to the UK that it was working on a new version of the contact tracking app that incorporated the Apple-Google software tool.
"We have decided to join forces with Google and Apple to bring together the best parts of both systems," said Hancock.
However, Apple said, "We don't know what they mean with this hybrid model. They haven't talked to us about it."
He told the BBC he had nothing else to add.
Google said yesterday that it welcomed the government announcement.
A Downing Street spokesman said the government has continued to work closely with Apple and Google on the app and has done so since the beginning of development.
"We agreed with them to continue our work on estimating distance through the app we developed and we are working to incorporate it into their app," he said.
Apple and Google have not created an app.
What they created is a software tool that allows contact tracking apps to run more smoothly with iPhones and Android devices, but that doesn't store data centrally.
The UK wanted to archive the data because it claimed that it would be useful for scientists to monitor the spread of Covid-19.
Dr David Bonsall of the University of Oxford, who is an SSN app developer consultant, told the BBC that the technology giant had made a choice not to support the original UK model.
"In the end, Apple decided not to support the centralized system that had been developed by the UK since March, and six weeks before announcing its system with a decentralized model," he said.
"And this must be considered in our reflection on the situation that the United Kingdom now faces."
The now abandoned NHS app has been tested on the Isle of Wight, where it has been downloaded over 50,000 times.
However, it only recorded around 4% of the iPhones nearby.
The islanders have now been asked to eliminate it.
It is not the first time that the government has clashed with Apple on an app: in 2018 an app built to help EU citizens to ask to stay in the United Kingdom after Brexit also did not work properly on the iPhone.
On that occasion Apple eventually agreed to make the necessary changes to its system.
