Rehman Malik, Pakistan's interior minister, reiterated on Tuesday that the family could have been behind the abduction, but police said there was no evidence that relatives had been involved.
"Presently, we don't know about the suspects or culprits," Aslam Tareen, the regional police chief, said.
"He is quite well, he is playing, we have arranged some toys for him," said Tareen.
Tareen said he did not know whether a ransom was paid.
Sahil's relatives said they were delighted that he was safe and vigorously denied the claims that someone in the family was involved in the abduction.
Some relatives said Sahil was taken by robbers who stole jewellery and cash and demanded a $120,000 ransom.
Kidnappings of Westerners are rare in Pakistan, but abductions of locals are common.
|Tareen, the regional police chief, said he did not know whether a ransom was paid [EPA]
They are often related to family quarrels, love affairs, property disputes or simple quests for money - particularly for the wealthier victims - by criminal gangs, some of whom are connected to Islamist fighter networks.
Raja Saeed, Sahil's father, said the kidnappers stormed the house armed with guns and grenades, subjecting the family to a six-hour ordeal while he and his son were preparing to take a taxi to the airport and fly home.
Akila Naqqash, Sahil's mother, who had begged for his release, said her son can expect a "big party" when he returns home to Oldham, in northern England, although it was not immediately clear when that would be.
"I talked to him on the phone and I thought, 'that's my little boy', that's enough for me," Naqqash told BBC radio.
"The way he spoke to me was normal, like a normal little boy."
Naqqash said he had asked about his sisters and remarked how much he was missing his favourite toy.
"I am just waiting for my little boy to come back. No more crying, I just want to have a big party,"
Celebrating relatives in Pakistan handed out sweets in Jhelum to friends, neighbours and family members offering their congratulations.
"I am thankful to God that he has been recovered. We are so happy," Tasneem Bashir, Sahil's grandmother, said.
Adam Thomson, the British high commissioner to Pakistan, said he was "simply delighted that Sahil has been released safe and sound.
"I know that his family must be overjoyed following almost two weeks of terrible anxiety and uncertainty.
"The top priority for the high commission now is to ensure he is reunited with his parents as soon as possible and to help with his return to the UK".
Thomson said although a "little tired", Sahil was "in good spirits".
British officials gave no details on exactly how Sahil had been recovered, saying he was in the care of Pakistani authorities and his uncle, and that the British consul was with him.