Schedules released by the BBC showed the programmes will overlap for 65 minutes when Strictly kicks off for a new series with its first Saturday show on September 19.
ITV is understood to be "disappointed" at the BBC's "aggressively competitive scheduling", according to insiders.
The two shows have occasionally had up to half an hour's overlap, although during the last series BBC1's Strictly usually finished before its ITV1 rival began, with no shows starting any later than 6.45pm.
Strictly will start at 7.25pm when it returns for its first Saturday edition.
The BBC put the later time down to a new series of Merlin beginning.
But an ITV source was critical of the move: "Given that millions of people enjoy watching both shows, such aggressively competitive scheduling is neither in the interests of the licence fee-paying public, nor viewers generally."
A BBC spokeswoman said: "Strictly Come Dancing and X Factor have successfully co-existed on a Saturday night for many years.
"This year is no different. Indeed there is even more choice for viewers with Strictly launching on a Friday and ITV scheduling its results show on a Sunday."
Among competitors for the new Strictly series are Martina Hingis, Jo Wood, Joe Calzaghe and Natalie Cassidy.