But a 2015 inspection report shows a target of 12,000 voluntary departures in 2015/16 was set by the department.
Labour MP Sally Jones, who is a member of the Home Affairs Select Committee, said the disclosure that there were targets for voluntary departures raised new questions for the Home Office.
She expressed concern that targets had led to the creation of a climate where “things have been overlooked on the basis of trying to get people out of the country”.
She told the BBC Radio 4 Today programme: “I think we need some clarity around what drivers were pushing the workforce to make the decisions that they made.
“We know that there was a target to reduce immigration, we know that there was limited capacity to reduce the number of people coming in, and now it appears there were targets to increase the number of people going out.”
Culture Secretary Matt Hancock denied that targets had led to people being arbitrarily removed.
“As far as I understand it, it has never been Home Office policy to take decisions arbitrarily to meet the target. There are rules around immigration. Immigration needs to be controlled but the rules also need to be fair,” he told the Today programme.
During an intense grilling at the Commons Home Affairs Committee on Wednesday, the Home Secretary admitted she was “surprised” she did not realise the scale of the problem earlier.
Rudd said no one from the Windrush generation had been wrongly deported “as far as we can see at the moment”.
Theresa May has steadfastly stuck to the immigration target first set by David Cameron - despite opposition from within her own party.
Asked on Wednesday whether the target led to people who have a legal right to live in the UK being targeted for deportation, Rudd said: “I don’t think that’s got anything to do with it.”
“It’s wrong to think the net migration target is the problem here. The problem here is that people were not properly documented,” she said.
Asked if she had told May to ditch the target, Rudd said: “I have not discussed that with the prime minister.”
She added: “I have private conversations with the prime minister which will stay private.”