The statement, purportedly sent by a British member of IS, said it was "outrageous" to suggest the Mannan family from Luton had been kidnapped and forced to join the group.
The BBC has not been able to verify if the statement is genuine.
A friend of a teenager among the 12 said he thought he had been "tricked".
The family, who have not been seen since 17 May, includes three children aged between one and 11. Police have previously said they may have travelled to Syria.
The statement is accompanied by two photos purportedly of family member Muhammed Abdul Mannan, which have not been independently verified.
It comes as a video apparently released by the IS group showed 25 men being shot dead in the ancient Syrian city of Palmyra.
The missing family is:
The statement, passed to the BBC by a Briton fighting with IS, said the family had arrived in a land that was "free from corruption and oppression" and had not been "commanded" to join by a single person but by the "Khalifah of the Muslims".
It said: "We say to those that are concerned for our safety to put your hearts at rest for we feel safer than we have ever felt before."
It went on to urge Muslims to "race to your state".
Nazrull Ali, a school friend of 19-year-old Mohammed Toufique Hussain, who is said to be among the 12, said he did not believe the statement.
"That doesn't seem right to be honest. I don't think they would say stuff like that," he said.
"I don't know but I heard they [IS] could make you say whatever they want, obviously if someone puts a gun to your head what would you say?" he said.
"He would have said bye to all of us properly and I'm telling you, he did not know that he was going to Syria. I know it wasn't him, I think he's got tricked into it. It wasn't his idea, definitely."
The Islamic State group has seized large swathes of Iraq and Syria since last June, becoming notorious for its brutality, including mass killings, abductions and beheadings.
On 29 June 2014 it announced the formation of a caliphate - a state governed in accordance with Islamic law or Sharia, by God's deputy on Earth, or caliph.
Shiraz Maher, senior fellow at the International Centre for the Study of Radicalisation at King's College London, which tracks the movements of foreign fighters in Syria and Iraq, said there was an element of propaganda to the statement.
Mr Maher said he was told by a British fighter that the family had chosen to release the statement to show it was their decision to move.
He said the broader project of IS was to persuade women and families to join them.
"They never wanted just fighters, I think that's a misnomer," he said.
The family was reported missing to police by two sons, understood to be Mr Mannan's from a previous marriage, who live in Luton.
They flew to Bangladesh on 10 April, police said, and then to Istanbul on 11 May.
They were due back at Heathrow three days later but failed to return.
It is believed Ms Khanom had links to banned Islamist group al-Muhajiroun, which had members in Luton.
Meanwhile, it has emerged that two sisters from another Luton family were prevented from flying to Bangladesh by counter-terror police shortly before the family of 12 went missing.
Officers seized the passport of one of the sisters, who is in her 20s and is said to be linked to the banned radical group Al-Muhajiroun.
They allowed the second sister to fly out to Bangladesh to join her family two or three days after the stop, between late March and early April.
Separately, two of three east London teenagers who fled to Syria to join IS have married militants, a lawyer for their relatives said on Saturday.
Bethnal Green Academy pupils, Shamima Begum, 15, Kadiza Sultana, 16, and Amira Abase, 15, fled Britain in February to join the militant group.
Hundreds of Britons have travelled to support or fight for jihadist organisations in Syria or Iraq. Last month three sisters reportedly took their nine children to Syria.
A UK family of 12 who went missing have joined so-called Islamic State and feel "safer than ever", according to a statement said to be on their behalf.