Chief executive Sean Doyle urged the Government to “set an example” and “be ambitious” in developing systems which enable people to travel overseas.
This includes the use of digital technology to verify the vaccination and test status of passengers, he explained.
Mr Doyle said the UK can be “very proud” of the creation of the Oxford AstraZeneca vaccine and the relatively high number of people who have already received a Covid-19 jab compared with other countries.
“We’re making great progress in Britain in dealing with the pandemic,” he told reporters.
“It’s fair to say that Britain has developed a really strong leadership position in coming out the other end of the pandemic.
“What we want to make sure is that we also take that leadership position into restoring travel and restoring the economy.”
He added: “We can be ambitious, and we can pursue this opportunity in a way that others could follow.”
British Airways is trialling the use of a “mobile travel health passport”, produced by VeriFLY, to enable passengers travelling from London to the US to prove they meet US entry requirements before they board a flight.
Mr Doyle, who replaced Alex Cruz as the carrier’s boss in October 2020, warned that the UK will find it “very hard” to reopen for business and investment if travel remains heavily restricted.
It is “pretty obvious that governments and countries want to accept British travellers again”, Mr Doyle said, citing recent announcements from France, Spain, Portugal, Greece and Cyprus about easing border restrictions.
But “rapid action” and “global coordination” is required, according to Mr Doyle.
“We do need to work across multiple governments and jurisdictions, and I think we have a great opportunity to drive that leadership position.
“For us, it’s quite simple. I think people who’ve been vaccinated should be able to travel without restriction, and those who have not been vaccinated should be able to travel with a negative test result.
“It’s worth reflecting on the fact that testing availability and testing solutions are in a far better place than they were a year ago, and they’re much more affordable.”
British Airways’ owner IAG suffered a pre-tax loss of 7.8 billion euros (£6.8 billion) in 2020 as demand for travel collapsed due to the virus crisis.
Mr Doyle admitted it has been “a pretty brutal and tough 12 months”.
But he said British Airways has seen a “surge” in bookings for flights from May 17, which is the earliest date that foreign leisure travel could be permitted for people living in England.
He added: “The summer holiday is something that people are holding out hope for.”
The Government’s Global Travel Taskforce will provide a report to Prime Minister Boris Johnson on April 12 setting out recommendations for how and when overseas trips could resume.