David Cameron and his wife Samantha have passed on their thanks for the messages of support after the death of son Ivan, their "beautiful boy".
William Hague, standing in for the Conservative leader as PM's questions was suspended, said Ivan had brought "joy and love to those around him".
Gordon Brown said everyone's thoughts and prayers were with the family.
Six-year-old Ivan, who had cerebral palsy and epilepsy, died at St Mary's Hospital in Paddington, London.
Mr Brown, who suggested suspending the weekly Commons clash as a mark of respect, said every child was "precious and irreplaceable" and that the death of a child "was something that no parent should have to bear".
The prime minister, whose daughter Jennifer Jane died aged just 10 days in 2002, paid tribute to Ivan saying: "I know that in an all too brief life, he brought joy to all those around him and I know also that for all the days of his life, he was surrounded by his family's love."
Mr Hague told MPs he had spoken to Mr Cameron, who wanted to pass on the family's thanks for their messages of condolence and say how "hugely grateful" they were to the NHS staff who had helped Ivan throughout his life.
Mr Hague said: "Ivan's six years of life were not easy ones. His parents lived with the knowledge for a long time that he could die young, but this has made their loss no less heart-breaking...
Together they will come through this and treasure the memories they have of Ivan
"Ivan suffered much in his short life, but he brought joy and love to those around him and, as David himself has said in the past, for him and Samantha he will always be their beautiful boy."
Deputy Lib Dem leader Vince Cable, who is standing in for Nick Clegg, also expressed his party's condolences in a short statement, appealing for the family to be given space to "grieve and cope with this tragedy that they've experienced".
Commons Speaker Michael Martin then suspended the sitting until 1230 GMT "as a mark of respect to Ivan".
MPs from across the political spectrum have expressed their condolences to Mr Cameron, who has been leader of the UK's official opposition since 2005.
And Buckingham Palace said the Queen had sent a private message of sympathy.
Shadow Chancellor George Osborne, a close family friend, said that although Ivan had often been hospitalised in the past, his death had been sudden, just 45 minutes after being admitted to hospital and had "caused a profound shock and, of course, huge grief".
He told BBC Two's Daily Politics: "Even with his very severe problems, he was part of family life and they are obviously absolutely devastated by what's happened."
Gordon Brown, William Hague and Vince Cable offer their condolences
But he added that the Camerons were a "strong" family and that "together they will come through this and treasure the memories they have of Ivan".
Mr Cameron, who has two other children Nancy, five, and Arthur, three, had been an MP for Witney, in Oxfordshire, for less than a year when Ivan was born in April 2002.
He suffered from Ohtahara syndrome, a very rare form of epilepsy characterised by spasms which start in the first days of life. Some children can suffer as many as 100 seizures every day.
Describing the moment when he learned of Ivan's disabilities, Mr Cameron told the Sunday Times in 2005: "The news hits you like a freight train.
"You are depressed for a while because you are grieving for the difference between your hopes and the reality. But then you get over that, because he's wonderful."
Friends have said the experience of caring for Ivan broadened Mr Cameron's political outlook and made him a passionate supporter of the NHS, which helped provide the round-the-clock care Ivan needed.
"The problems that Ivan had in some way shaped that family and shaped David as a person," said George Osborne.
In a 2007 speech, Mr Cameron described how he cared for the "severely disabled" Ivan.
Ivan Cameron with Samantha Cameron
"It's what I do at the start of each day. It's sharpened my focus on the world of care assessments, eligibility criteria, disability living allowance, respite breaks, OTs, SENCOs, and other sets of initials.
"But I would not dare to call myself a carer. The work that full-time carers or those with little extra help do is unbelievable."
But he also spoke of how proud he was of Ivan, saying in another interview: "He is a magical child with a magical smile that can make me feel like the happiest father in the world.
"We adore him in ways that you will never love anybody else, because you feel so protective."
The Camerons have asked that, rather than sending flowers, people send donations to Mencap or the Friends of St Mary's Hospital.
Shadow Foreign Secretary William Hague will stand in for Mr Cameron as Conservative leader while he takes time off, it is understood.
A Number 10 dinner later to mark the unveiling of a portrait of Baroness Thatcher which Mr Cameron had been scheduled to attend has also been cancelled.
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