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Thousands of travellers stranded at European airports started to see signs of operations getting back to normal on Tuesday, although delays were still lengthy.

By late afternoon, London's Heathrow Airport managed to reopen its second runway, which had been closed since 13 centimetres of snow fell on Saturday.

But airlines were still operating on greatly reduced schedules. Passengers were being told not to go to the airport unless their flights were confirmed to be operating.

Air Canada, which uses Heathrow's Terminal 3, said its normal schedule of flights would resume Tuesday evening but warned travellers it could take more than a week to clear a backlog of passengers from previously cancelled flights.

Meanwhile, Frankfurt airport in Germany was forced to cancel and delay flights for several hours early Tuesday after a heavy snowfall.

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Earlier, British Prime Minister David Cameron said the "extensive disruption" at Heathrow is understandable, given how much snow has fallen. But he also said he is "frustrated on behalf of all those affected that it's taken so long for the situation to improve."

Cameron, speaking to reporters at a pre-holiday news conference Tuesday, said changes have been made to help the airport get people moving.

"The people stuck there are having an incredibly difficult time, especially just a few days from Christmas, and everything must be done to either get them on holiday or get them home," Cameron said.

The prime minister said normal restrictions on nighttime flying have been relaxed to help ease the backlog at airports.

He said the government has offered military assistance to British Airports Authority, which operates Heathrow. Airport operators said they were grateful for the offer but didn't need the help because they had brought in extra staff and contractors to help with the recovery, The Associated Press reported.

Stranded family gives up

Jonathan Pinto and his family were supposed to be in Mangalore, India, on Tuesday to celebrate an upcoming wedding with extended family.

But after dealing with days of delays at Heathrow Airport, the family has given up its travel plans and decided to return to Toronto.

"Well, over the last couple of days we've been looking for flights back home," he told CBC's Metro Morning.

He said he finally managed to book a flight around 2 a.m. London time. The family will head to Boston on Christmas Day and will continue on to Toronto on Boxing Day.

He said his family gave up on plans to travel to India after spending 10 hours stuck in a plane parked on the tarmac at Heathrow. They spent one night on the terminal before moving to a nearby hotel.

"We just decided we need to go home and kind of recuperate," Pinto said Tuesday as he packed his bags to head to yet another hotel.

He said he hopes to explore London while he waits for his flight, but even this plan has a hitch.

"Because we were supposed to go to India, we didn't pack any winter clothes."

Malcolm Robertson, a spokesman for the  British Airports Authority, told CBC News the airport is working with airlines to gradually increase the capacity "and get as many people moving as we can."

Robertson said crews cleared the runway as quickly as possible after the major snowfall on Saturday, but a drop in temperature created dangerous, icy conditions that have been difficult to clear.

"We have invested recently in new snow-clearing equipment," he said. "Having said that, we will clearly look at what has happened here, and what the future outlook is and if we have to buy new equipment we will."

Simon Calder, a travel writer, said he's worried the damage to Heathrow's reputation will last.

"Now I fear that business just evaporates, because who travelling globally would ever want to buy a connecting flight via Heathrow?"

CBC's Tom Parry said there were still long lines of people waiting outside Heathrow's Terminal 3 on Tuesday.

"There is a little more infrastructure here today to help people," he said. "The Salvation Army has set up a station where they are giving out tea and coffee to people, helping them keep warm."

He said airport officials have set up heated tents where they are informing anxious travellers about flight schedules.

Eurostar, which links England to France and Belgium by train, also advised passengers to cancel their trips in the coming days unless travel is absolutely necessary. They would receive a full refund.

The company said trains were running with speed restrictions in both England and France as a precaution because snow and ice stirred up by trains could damage the underside of the carriages.

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Travellers sleep on camp beds provided by airport operator Fraport at Frankfurt airport on Tuesday. ((Alex Domanski/Reuters))

Outside London's Eurostar terminal, the line of travellers waiting for trains snaked several hundred metres from the station, down the street and all the way to the British Library.

The delays aren't limited to London — fresh snowfall forced Frankfurt airport, Germany's largest, to suspend takeoffs and landings for a few hours early Tuesday.

Airport authorities said flights were suspended a little after 5 a.m. local time. The first runway was reopened at about 8:30 a.m. local time. Frankfurt has seen hundreds of cancellations over recent days, often a result of disruption elsewhere in Europe, including major problems at Heathrow.

In Paris, officials said air traffic at Charles De Gaulle Airport and Paris-Orly Airport were "resuming progressively" but cautioned that further disruptions should be expected. 

At Gare du Nord train station in Paris, several hundred passengers waited in an orderly line stretching to the back of the station. Another several hundred lined up at the top of an escalator.

Schiphol Airport in Amsterdam said it was also experiencing weather-related delays.

With files from The Associated Press