The transport secretary has said people arriving in the UK from countries with low coronavirus infection rates could be exempt from new quarantine rules.
The government plans to ask most visitors to isolate for 14-days.
Initially, the quarantine – which is expected to come into effect in early June – will be “a blanket solution”, Grant Shapps said.
However, countries with a low infection rate could be exempted from the rules in the future, he said.
Mr Shapps promised the final details of the quarantine plans would be “released soon” and said there were “active discussions” on the policy. Ministers have indicated that Ireland will be exempt.
However, the proposed rules have already attracted the anger of some senior figures in the aviation industry.
Airlines worry that people would be put off flying if they are required to self-isolate at a private residence for two weeks once they arrive in the UK.
Earlier on Monday, the boss of Ryanair, Michael O’Leary, described the quarantine plans as “idiotic”. He said the policy had “no credibility” and predicted that it would be gone by June.
“It’s idiotic and it’s un-implementable. You don’t have enough police in the UK,” he told BBC’s Today programme.
Speaking in the Commons, Mr Shapps said: “We should indeed consider further improvements, for example things like air bridges enabling people from other countries who have themselves achieved lower levels of coronavirus infection to come to the country.”
“So those are active discussions but will go beyond what will initially be a blanket situation.”
Greece has called for an exemption from the proposed quarantine rule.
Speaking to the BBC’s Coronavirus Newscast, the country’s tourism minister, Harry Theoharis, urged the UK not to require Greeks to isolate when they arrive. In return, he said, Brits could enter Greece.
Last week, the government was forced to deny that travellers from France would be exempted from the planned coronavirus quarantine measures.
Initially, a joint statement from the British and French governments said no quarantine measures would apply.
“No quarantine measures would apply to travellers coming from France at this stage; any measures on either side would be taken in a concerted and reciprocal manner,” says the statement, which was published on the government’s website on 10 May.
“A working group between the two governments will be set up to ensure this consultation throughout the coming weeks.”
The policy attracted a warning from the EU not to single out one nation, while some experts suggested it would prove unworkable.
But on Friday, the prime minister’s spokesman insisted there was no French exemption, and that the original statement referred to the need for cooperation to manage the common border between the two countries.