Britain's National Air Traffic service says that after Scotland's airports and airspace reopen, London's airports - including Heathrow - might be able to open later in the day.
Millions of travelers have been affected since the Icelandic volcano began erupting last week. It is the second time that the volcano has erupted in a month after lying dormant for about 200 years.
White House spokesman Robert Gibbs says the U.S. government is trying to help some 40,000 Americans who are stranded in Britain and trying to get home.
"We are working closely with the State Department to examine all the opportunities that we have to speed this process along," said Robert Gibbs. "And the understanding that some people may have gone on vacation, they are running out of medicine, they don't have a place to stay."
The announcement of the plans to progressively resume flights comes as the aviation industry is criticizing government officials for their handling of the situation. It is estimated that the airline groundings have cost the industry more than $1 billion in lost revenues.
Michael O' Leary, the head of Ryanair, Europe's major low-cost carrier, cautiously welcomed the decision to resume flights.
"We welcome the opening of U.K. airspace on a graduated basis," said Michael O' Leary. "But frankly, this thing could change on an hour-by-hour basis, depending on what happens with the volcano in Iceland."
A statement late Monday from the the British National Air Traffic Service highlighted that uncertainty. It said the eruptions have strengthened and a new ash cloud was heading toward Britain.
Klaus Walther, spokesman for Lufthansa, cautions that it will take some time for air traffic to return to normal.
Walther says it will take some time because Lufthansa has not yet returned to normal flight conditions, which would enable it to arrange 1,800 flights per day. He adds that for the next few weeks, the airline will be following special rules and permissions agreed upon between the Federal Office of Civil Aviation and German airlines, and that safety will be the highest priority.
The agreement reached by EU transportation ministers creates three zones - a no fly zone immediately over the ash could, a caution zone where there is some contamination and an open skies zone.
Planes flying in the caution zone will be subject to engine inspections for damage upon landing.
Experts say that although ash and gases from volcanic eruptions can damage the exterior of a plane as well as its air filtration system, the most serious threat is to its engines, which could fail during flight.