Robin Cook's widow has paid tribute to her husband claiming "his love was the greatest gift I will ever receive".
It is hoped the post mortem will reveal the cause of Mr Cook's death
Gaynor, 48, who was at the former foreign secretary's side when he died, also praised her husband's "generosity, tolerance and integrity".
Mr Cook, 59, collapsed while walking in the Scottish Highlands on Saturday and was pronounced dead after being airlifted to hospital.
A post mortem examination is being held to determine the cause of death.
Mr Cook's sons Christopher and Peter, from his marriage to first wife Margaret, have travelled to Scotland from their homes in England.
Gaynor Cook said: "At this terrible time, I have been deeply touched by the many, many messages of support I have received and Christopher, Peter and I want to thank everyone who has given and offered help.
"I loved and admired my husband - for his generosity, his tolerance, his integrity and his great joy in life."
Mr Cook was pronounced dead at Raigmore Hospital 90 minutes after collapsing on Ben Stack.
The post-mortem examination, which is expected to be completed on Tuesday, will aim to establish whether the Livingston MP died from an illness or injuries sustained in the fall.
Funeral details were due to be announced on Monday.
A Downing Street spokeswoman said the prime minister was unlikely to break off from his holiday for the funeral, with his deputy, Mr Prescott, likely to attend instead.
She added that if a memorial service was held later in the year, Mr Blair would attend.
Family friend Jim Devine, Mr Cook's election agent, told BBC Radio's Good Morning Scotland programme: "I have to meet with the funeral directors and various people this morning, and we will be making that announcement this afternoon."
Mrs Cook formally identified her husband's body on Sunday.
The couple had been enjoying a trip to the north of Scotland when Mr Cook collapsed with a suspected heart attack.
Despite attempts by Mrs Cook and a fellow walker to resuscitate Mr Cook, the MP was pronounced dead at 1605 BST on Saturday, five minutes after he had arrived at the hospital by coastguard helicopter.
The Cooks are thought to have been staying in the village of Durness, near Cape Wrath - one of the most northerly inhabited localities on mainland Britain.
On Saturday afternoon, Mrs Cook had alerted another walker to her husband's collapse and the man contacted the emergency services at about 1415 BST.
Graham MacKenzie, the ambulance control room manager at Inverness, told how staff went through the resuscitation procedure with the man on his mobile phone.
Gaynor Cook spent about 15 minutes at Raigmore Hospital
Mr MacKenzie said: "We first established what had happened, that he had collapsed and then we asked was he conscious, he answered no, was he breathing, again no.
"Our priority was to re-establish breathing so CPR instructions were given for the best part of nearly 50 minutes until the helicopter arrived."
Coastguard George Chrossan, who had to be winched down from the rescue helicopter, said Mrs Cook told him her husband had stopped breathing about 40 minutes beforehand.
It is understood Mrs Cook walked back down the 2,365-ft peak after her husband was on board the helicopter and was comforted by friends in Durness prior to travelling to Inverness.