Freed British couple Paul and Rachel Chandler have been told that his father died while they were being held hostage by Somali pirates.
The couple, whose yacht was boarded off the Seychelles in October 2009, say they will return home "very soon".
Paul, 60, and Rachel Chandler, 56, from Tunbridge Wells, Kent, are at the British High Commission in Nairobi.
They have asked for privacy as they "adjust to the situation" and "come to terms" with their loss.
In a statement, they said: "We thank you all for your concern and interest.
"We have just learned that Paul's father died in late July, and we obviously need to come to terms with that.
"We do not intend to give any press interviews or make any further statements until we have had time to adjust to the situation and we would appreciate it if you would give us and our families some space, and respect our privacy for the moment."
News of their release emerged on Sunday, and they were initially taken to Adado, central Somalia, near the Ethiopian border.
Their 13-month ordeal was reportedly ended by the payment of a ransom.
BBC security correspondent Frank Gardner said the sum paid for their eventual release had been "the best part of $1m" (£620,000), although there has been no official confirmation of this.
A Downing Street spokesman said the prime minister had spoken by telephone to Paul Chandler and expressed "joy at their release and praised their bravery".
David Cameron gave assurances the government would give the couple all the support they needed and would reunite them with their family soon, the spokesman added.
He also stressed no UK aid money to Somalia had been diverted to help pay the couple's ransom.
"The government has a policy on ransom payments which is we don't do them," he said.
The Chandlers, who spent 13 months held hostage in harsh conditions and intense heat in rural Somalia, said they had been beaten when they refused to be separated during their time in captivity.
"We were really distraught, we were very frightened at that point," Mrs Chandler said after arriving safely in Kenya.
Both Mr and Mrs Chandler, who are experienced sailors, said the worst time had been leaving their yacht in the first place.
They had been sailing from the Seychelles towards Tanzania as part of a longer voyage.
"We had to abandon our home and boat... in the ocean," Mr Chandler said.
The couple said they had only the vaguest idea of how the rescue had come about having had no communication since the middle of June with the outside world.
Mr Chandler said they had been driven across Somalia to Adado and were later transferred to Mogadishu and then on to Kenya. The couple have undergone medical checks in Nairobi.
Details of the release were not given by the Chandler family in the UK, who issued a statement saying: "The family believes it would be irresponsible to discuss any aspect of the release process as this could encourage others to capture private individuals and demand large ransom payments, something that we are sure none of us wants."
Earlier this year their captors threatened to kill the couple if their demands for $7m (£4.4m) were not met.
A payment of about $430,000 (£267,000) was made to the pirates in June, but did not result in the release of the Chandlers.
Media speculation was thought to have influenced the pirates, and so the family opted for a super-injunction banning media coverage of the kidnap.
Our correspondent said it was thought unlikely any of those responsible would be brought to justice in Somalia, a country without an effective government since 1991.
Former Church of England envoy Terry Waite, held captive in Lebanon for nearly five years before being released in 1991, advised the Chandlers to "just take time out" and tell their story to a "trained listener".
He said that "then you have a chance to manage it, rather than being managed by it".
He also told BBC Radio 4's Today programme that there would be various things they would have to come to terms with including the ransom.
"Will they feel obliged to somehow give the money back to those who have paid for their release?" he added.