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Gemma Wilkinson, a former charity worker, took legal action in an attempt to force Anjum to reveal the whereabouts of her daughter Atiya.
Anjum, who represented himself at the latest court hearing, indicated that Atiya was in Pakistan or Iran but said he did not know her exact whereabouts.
Mr Justice Moor said he was sure Anjum was lying.
Razwan Ali Anjum was handed a fourth consecutive jail term by a High Court judge in April after he refused to reveal where his daughter was.
Mr Justice Moor imposed a 12-month prison sentence after he found him in contempt of a High Court order instructing him to disclose her whereabouts.
He said Anjum, who is in his late 20s, would not be eligible for release until he had served at least six months.
Judges have previously imposed jail terms of two years, 12 months and another 12 months in the hope that Anjum would provide information.
They have re-jailed Anjum as each sentence neared its end.
The mother of a missing girl abducted by her father says she prays her "little bundle of joy" is safe and well, three years after she was taken.
Gemma Wilkinson from Ashton-under-Lyne, Greater Manchester, said not knowing five-year-old Atiya is even alive is an "absolute nightmare".
The 32-year-old is appealing today for information on her whereabouts.
Atiya vanished in November 2009 after going to stay with her father, Razwan Ali Anjum.
The former insurance salesman said he was taking Atiya to Southport.
Instead he took her to Lahore, Pakistan, and told Ms Wilkinson that she was "never going to see Atiya again", courts have heard.
Latest ITV News reports
The mother of a missing girl abducted by her father has renewed an appeal for information find her.