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Nimet Cubukcu, the minister in charge of women and family affairs, said the television program is timed to air at around the same time the European Union is scheduled to release a report on Turkey's progress toward membership.
"It is obvious that in this situation, Sarah Ferguson is trying to leave Turkey in the midst of a smear campaign," Cubukcu said.
Ferguson went undercover to visit two state-run orphanages in Ankara and Istanbul to expose the conditions, Britain's Press Association said.
At the Saray institution for disabled children near Ankara, the Duchess and a team reporting for British television ITV1's "Tonight" show found children tied to their beds or left in cots, the Press Association reported. Ferguson also visited orphanages in Romania for the program.
Details of the show were also reported in most Turkish newspapers Monday.
In London, Kate Waddington, a spokeswoman for the Duchess denied Ferguson had any political motives.
"The Duchess of York has never got involved in politics and never intends to," Waddington told The Associated Press by telephone. "Her sole interest is in the welfare of children - abled and disabled children."
ITV spokeswoman Julia Fields said: "This is a valid area of public interest at a time when the UK government is endorsing the accession of Turkey into the EU, a process which is conditional in part on Turkey improving its human rights record with children."
Cubukcu said Turkey was probing all kinds of "human rights abuses and misuse of authority" in the institutions visited by the Duchess.
"Our ministry has no tolerance at all for rights abuses in its institutions," she said.
Neriman Kocak, a director for the Saray orphanage, acknowledged that the facility was old and in need of an overhaul, but denied that the children were tied to their beds.
Turkish Foreign Minister Ali Babacan said the whole process in which the images from the documentary were filmed was unacceptable.
Diplomatic sources told the Hurriyet Daily News (HDN) that Ankara conveyed its uneasiness on the issue to London in writing. Turkey objected to the method, not the content, they said.
The program, called "Duchess and Daughters: Their Secret Mission" was scheduled to be aired in Britain on Thursday, ITV said.
The EU is scheduled to release this month its annual report on Turkey's progress on reforms needed to join the EU.