Priti Patel, the home secretary, has said the Conservatives would reduce immigration, as one of her ministers acknowledged people had felt “let down” by the party’s failure to hit its targets in the past.

Patel said levels of immigration would be lower but clearly dropped David Cameron’s failed target to cut net migration to the tens of thousands.

“We will reduce immigration overall while being more open and flexible to the highly skilled people we need, such as scientists and doctors,” she said. “This can only happen if people vote for a Conservative majority government so we can leave the EU with a deal.”

Following the announcement, the Home Office minister Brandon Lewis told the BBC he recognised the Tories had failed to keep promises in the past on reducing immigration.

“I recognise that people, including myself when I was immigration minister, have talked about reducing migration and net migration for years; we’ve not done that. And … that’s let people down. Labour obviously let the people in from all over Europe before when they were in government,” he said.

“People are always going to question whether this is doable and there are two key differences here: one is we need to be able to leave the EU, but also with a points-based system – one of the things we’ve not been able to do before, because we’ve not had a good Conservative majority.”

The Conservatives are seeking to make immigration a major dividing line between the party and Labour, as the opposition has not yet published its policy and is divided about backing free movement or a more controlled policy.

Patel claimed immigration would “surge” to 840,000 if Jeremy Corbyn became prime minister, but Labour said this claim was “fake news” and came from the “make-believe research department”.

Labour has not yet released its immigration policy but members voted at the party’s autumn conference to maintain and extend free movement.

In a Guardian interview on Wednesday, Len McCluskey, the Unite general secretary, said shadow cabinet members should not upset Labour’s carefully crafted Brexit position during the election and that he would oppose any attempts to extend free movement as voted for in Brighton.

The Tories said analysis of research into the conference proposals suggested net migration could increase to 840,000 a year under Corbyn. The party said the analysis was based on official figures and the government’s own methodology.

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According to the party, the research shows extending free movement to the rest of the world would result in average net immigration to the UK of 840,000 a year over the next 10 years. “This is equivalent to the combined populations of Manchester and Newcastle moving to the UK every single year,” the Conservatives said.

“This means that levels of net migration would more than treble if Labour introduced their proposals for completely open borders.”

The Tories said the analysis was “deliberately cautious and is likely to provide a significant underestimate of net inflows from non-EEA countries under Labour’s plans”.

The party also said maintaining free movement with existing European Economic Area members would result in average net immigration of 260,000 a year over the next decade.

Patel said: “Under Corbyn’s Labour, immigration would surge and put huge strain on schools and our NHS. Jeremy Corbyn has no credible plan for how to deal with the consequences of his open borders policy.”

Diane Abbott, the shadow home secretary, said: “This is more fake news from the Conservative party’s make-believe research department. Unlike the Tories, we won’t scapegoat migrants or deport our own Windrush-generation citizens. The damage done to our society has been through damaging Conservative cuts to our public services, not by EU nationals coming to work in them.”

Labour is also arguing the Conservatives have misinterpreted the conference motion, saying there was no mention of extending free movement to new geographic territories beyond EU countries.

The party said the motion supported extending freedom of movement rights – for example, a British citizen or someone with the right to live and work in this country would have the right to a family life, including the right to bring their spouse here.

Christine Jardine, the Liberal Democrat home affairs spokeswoman, accused Patel of a “Trumpian agenda” on immigration.

“This country needs people to come here to keep our NHS and so many sectors properly skilled and staffed. The Conservatives’ approach to immigration is an insult to the millions who have come to the UK and made it their home. Immigration brings so much to our communities, culture and economy,” she said.

“Patel’s comments this morning show that the Tories only care about arbitrarily reducing immigration numbers with no regard for the consequences. Our public services, including our NHS, rely on the contribution that immigrants make. But the Tories are willing to put this at risk just to pursue a nationalist Trumpian agenda.”