Brandon Lewis, the ex-immigration minister, said Ms Rudd set an "ambition" to ramp up the removals by 10 per cent.
But he insisted she didn't know that specific targets for the precise number of migrants being deported were used by Home Office officials.
Labour accused the Tories of "hiding behind semantics" in their response to the ongoing row.
Ms Rudd last week told Parliament she didn't know about the immigration removal targets in the wake of the Windrush generation crisis.
But a memo which was leaked on Friday showed she WAS told about the targets.
Today Mr Lewis, now the Tory party chairman, said he had seen the memo but never discussed it with Ms Rudd.
He told the BBC's Andrew Marr Show: "I was working with her on a weekly basis to make sure that we were doing everything we could – working with the police, working with local government – to help vulnerable people, to crackdown on criminals, and to remove more people who are here illegally.
"Yes, I did talk to the Home Secretary about that and the overall work that we were doing and the overall ambition to see an increase in numbers, but not on the detailed numbers and targets.
"What the Home Secretary was very aware of was her ambition to see an increase in the number of people who were being here illegally that we were removing, particularly those foreign national offenders.
"Those internal targets were not in the memo and not figures that she was aware of."
Labour's Diane Abbott said in response: "Brandon Lewis's attempt to save the Home Secretary's career by hiding behind semantics is insulting for the people who have been affected by the Tories' heartless policies.
"Beneath the spin, he let the truth slip and sealed her fate. Amber Rudd knew of the targets she pretended didn't exist.
"The Home Office was fully aware that lives were being ruined as a result of their 'hostile environment' but pressed ahead anyway. It's time for Rudd to go."
Ms Rudd will make a statement in the Commons tomorrow in a bid to stop the row escalating.
Today Tory MP Ed Vaizey warned that after the Windrush scandal, "We have to work three times as hard to win back ethnic minority voters now."
Around 200 MPs have signed a letter calling on new legal guarantees to the Windrush generation, ensuring Caribbean-born Brits never again have their right to be here questioned.
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