Qantas Airlines is cleared today to fly its planes to London's Heathrow airport after several of the flights were suspended overnight due to fresh ash clouds from Iceland's Eyjafjallajokull volcano.

Although other airports in different countries resumed its operations, there are other airlines who are still very cautious to fly their planes.

Most of the airlines, including Qantas, are now assessing the damage and losses after a six-day shutdown.

Qantas revealed earlier that two of its planes at Heathrow were grounded after it received reports of a "significant meteorological report" of ash on the proposed flight path. One of its flights to Melbourne was canceled yesterday.

A flight to Sydney via Singapore took off this morning after Qantas received a memo of an all-clear sign.

Olivia Wirth, a Qantas spokeswoman, disclosed to the media that the airline has to accommodate 15, 000 passengers who were affected by the ash cloud.

"There will be delays in the coming weeks if the situation does not resolve and the ash cloud doesn't completely clear," she said. "We'll continue to operate around those (with an all-clear pathway). Obviously for us, we will be taking a very conservative approach to this."

Qantas said flights to Europe from Melbourne will resume this afternoon.

On the other hand, Singapore Airlines declared it resumed its airline activities and its first flights from London will arrive in Australia in the evening. Flights to other European countries will arrive the next day.

A one-week shutdown has cost Qantas a $2 million loss per day while the International Air Transport Association said it lost about $1.9 billion after a week without revenues.

European airlines are requesting for compensations from the European Union and national governments.

Scientists said there are still evidences of ash blowing out from the volcano beneath the Eyjafjallajokull glacier in Iceland; however, most of the ashes were blown into the atmosphere.

Iceland's president issued a warning that another volcano nearby, Katla, may also erupt soon.