Writing to home secretary Priti Patel, Abta chief Mark Tanzer reiterated quarantine would have a "serious impact" on demand for holidays and business travel.
He also stressed the wide-ranging knock-on impacts the measures would have on the UK economy beyond just the travel and tourism sector.
Abta says it is essential ministers bring forward a coordinated plan to restart international travel that allows businesses and consumers to plan ahead.
It wants the roadmap to detail how the government will "transition away" from the Foreign Office’s current advice against all non-essential travel worldwide.
The association is also calling on the government to place an urgent focus on safe travel corridors to establish quarantine-free travel links with countries with lower rates of coronavirus infection, and to publish the scientific and epidemiological advice that underpins the country’s quarantine policy – as well as any advice informing the first three-week review of the policy in late-June.
It comes after Tanzer last week attended an industry "roundtable" hosted by Patel, which was overshadowed by British Airways’s decision to snub the home secretary.
Abta believes with the sector facing a "prolonged" period of discovery, its ability to rebound will be dependent on several factors.
These include restoring consumer confidence and demand for travel; establishing common health and safety protocols; and encouraging insurance providers to start offering travellers cover again.
"This will require a strategic, cross-departmental approach from the government," said Abta, adding it welcomed Patel’s promise, made in the Commons lsat week, to pursue such an approach.
"We must restart international travel as soon as it is safe to do so," said Tanzer. "Businesses and customers would benefit from the government outlining when this is likely to happen.
"There are many livelihoods at stake, and bookings will only start to pick-up in earnest when people and businesses have a better idea as to what the government’s plan is to open up the UK and access to international destinations.
"This is going to take a coordinated approach, and Abta will continue to do whatever it takes to assist with this process on behalf of travel agents and tour operators across the UK who are desperate for a clearer direction for travel."
Tanzer added: “Of course, safety must absolutely come first, which is why the government also needs to set out clearly the relevant scientific advice and epidemiological factors informing decisions, including the quarantining policy before its review in three weeks.”
