Covid testing firms are facing a shortage of lateral flow tests, says Transport Secretary Grant Shapps.
He told MPs this was the reason for delaying the date when PCR tests will be removed for travellers returning to England.
The travel industry has called on the government to confirm when in October the rules will be changed.
Mr Shapps said it would take several weeks to switch from PCR tests to lateral flow tests.
Addressing the Transport Select Committee, he said the Department of Health was responsible for making the decision.
However, he stressed that his colleagues were aware of school half-term dates and understood the speed required to implement this change.
"But my understanding is that the ramp-up of supply of lateral flow [tests] through the private testing sector has some way to go [since] they have been almost entirely been involved in providing PCR [tests] currently," he told MPs.
When questioned by MP Ben Bradshaw about why this was an issue, since many test providers also offer lateral flow tests, Mr Shapps said it was a question of scale.
"We go from a situation where they are providing a low number of thousands [of tests], to probably millions of tests very quickly and need a few weeks to scale up on it," he said.
He added that the extra few weeks were needed for making sure the administrative switch-over when the rules changed went off without a hitch.
In August, the government warned more than 80 firms about misleading Covid test prices and removed 57 firms from its website.
The government has announced that "day two" PCR tests will no longer be required for fully vaccinated travellers returning to England in October.
Instead, they will be able to take a cheaper lateral flow test.
Under the new testing regime, people who have had both coronavirus jabs will not need to take a pre-departure test before leaving any country not on the red list.
Rory Boland, travel editor at Which?, warned of the potential shortcomings of the new system.
"Test providers have struggled to cope with demand for PCR tests for months, so if they cannot meet the demand for lateral flow tests, there is a real risk that the system will once again fail travellers.
"Travellers need a testing system they can rely on, meaning that tests are easy to access, affordable, and that they will receive a reliable service from their provider. The government must ensure that any changes to the system - including replacing PCR tests with lateral flow tests - ensure this".
Without a confirmed date, however, aviation firms have warned they stand to lose out on lucrative school holiday bookings.
Bosses have welcomed the travel changes that have been announced so far, including rule changes to US and UK travel that were confirmed on Tuesday.
But they argued that UK aviation had been severely hit during the summer because of the traffic light system and testing.
They said the UK lagged behind a much stronger market in the European Union, where passenger numbers rebounded to some 70% of 2019 numbers.