Kate and Gerry McCann said yesterday it was "heartbreaking" to have to accept that they would spend a third Christmas without their missing daughter Madeleine.

In a heartfelt Christmas message, the couple said they felt "great disappointment" that all their efforts to find the little girl had so far failed.

But they insisted that their resolve would not weaken and said they would "pursue all avenues" that could help Madeleine.

The McCanns posted the message on their official Find Madeleine website.

They said: "It is heartbreaking for our family to accept the likelihood of spending a third Christmas without Madeleine.

"Her absence is even more tangible at this time of year. It is difficult also to believe that another year has passed by.

"There is... a feeling of great disappointment when the one thing that we want so badly still eludes us."

The couple made an apparent reference to Goncalo Amaral, the former head of the Portuguese police investigation into their daughter's disappearance.

The couple have brought legal action against Amaral over his book about the case, called The Truth Of The Lie, which claims that Madeleine is dead and questions the McCanns' account.

The McCanns said: "Some people (thankfully in the minority) may have their own reasons and agendas for wanting to discontinue the search for Madeleine, and for others it may be easier or more 'convenient' to give up.

"For us, there is no option, no alternative. We long for our 'baby', our daughter, our sister, our granddaughter, our friend, our dear sweet Madeleine to be home."

The McCanns have released two new pictures on their website, one of which shows Madeleine playing with her younger sister Amelie at Christmas 2006, less than five months before she vanished.

Madeleine was nearly four when she went missing from her family's holiday apartment in Praia da Luz in Portugal on 3 May 2007 while her parents dined with friends nearby.