Jeremy Corbyn has refused to say if he wants the number of immigrants coming to the UK to rise or fall.
In an interview with the BBC, the Labour leader said people should be “realistic” about needing to fill jobs so the economy’s needs can be met.
He said: “Putting arbitrary figures on it as successive governments have done simply doesn’t work.”
The Tories say they would aim to cut overall immigration but will not set targets, if they win the election.
BBC home editor Mark Easton said immigration was “not the electoral issue it once was”, with pollsters saying it is at its lowest level of concern for almost two decades.
But he added: “Some communities remain concerned that foreign arrivals put extra pressure on public services and jobs, and those voters are often in the Labour seats that the Tories are looking to take.”
In an interview with BBC political editor Laura Kuenssberg on a campaign visit to Scotland, Mr Corbyn hinted that Labour would make it easier for families to bring relatives to live in the UK from overseas and for foreign workers to come to the UK .
He said Labour’s immigration policy was “based on fairness and justice, and on the economic needs of our society, and they are considerable”.
Mr Corbyn added: “We have to be realistic that in this country we have 40,000 nurse vacancies, we have a great shortage of doctors, we have shortages of many skills, and they cannot be met very quickly because we’re not training enough people, so there’s going to be immigration in the future.”
But asked again whether he wanted the figure to be higher or lower, the Labour leader just said: “I want our system to be decent, to be fair, and our services to be properly run and properly staffed.”
Freedom of movement
Mr Corbyn said a motion passed at his party’s conference, calling for “freedom of movement” – the right of EU citizens to live and work in any other EU country – to be maintained and extended after Brexit “doesn’t necessarily form part of the manifesto”.
This is despite his shadow home secretary, Diane Abbott, tweeting earlier about Labour’s “commitment” to the pledge.
Mr Corbyn said her remarks were specifically about those EU citizens with settled status – people who have lived in the UK for five years, applied to the Home Office, and have been given the right to stay in the country for as long as they like – and to aid the reunion of families.
But he added: “I have made my case very clear about the value of migration to our society, about the stability of people living in our society, about the horrors of the hostile environment created deliberately by Theresa May, and others, and the uncertainty that so many EU nationals have been put through.
“I think that uncertainty should finish, they should have guaranteed rights to remain in Britain.”
Mr Corbyn said Labour’s eventual policy on immigration would also depend on the outcome of Brexit – with his party promising to renegotiate a deal with the EU within three months after winning an election and putting it to the public against Remain in a further referendum.
He called the plan “a sensible approach”, adding: “I recognise why people voted Remain and why people voted Leave in different parts of the country and for different reasons – in my own communities where I represent and also all across the country.
“[But] I think that is actually a sensible approach that a very large number of people [have] come to think, well, at least somebody has been grown-up about this.”
Len McCluskey, the leader of the biggest Labour-supporting union, Unite, and a key ally of Mr Corbyn, has called for new employment policies to address concerns about freedom of movement.
Mr McCluskey told the BBC: “Labour’s policy will be to protect all workers – migrant workers as well as British workers. It will be done with labour market regulations.
“It won’t stop the free movement of labour. “It will effectively make certain that greedy bosses, agency companies, are not abusing working people.”
Net migration pledge
Mr McCluskey denied a newspaper report that he had told Jeremy Corbyn to take a tough line on free movement of workers.
More than 130 Labour candidates have signed a pledge to campaign to Remain in the EU – which would mean accepting the continuing right of EU citizens to seek work in the UK.
But Mr McCluskey stressed that Labour “is not a Remain” party and a referendum with a Leave option – “a fair deal” – would be offered to voters if Labour wins the election.
The Conservatives have said they will end free movement from the EU on 1 January 2021, if they win the election and get their Brexit deal through Parliament by 31 January.
The party made its promise to reduce “immigration overall” in a press release on Thursday, quoting Home Secretary Priti Patel, and reiterating its plan for a “points-based” immigration system, which would apply to EU and non-EU migrants.
However, in an interview later in the day, Mrs Patel was asked several times before saying the party would “look to reduce the numbers” through better immigration controls.
The Conservatives also are expected to ditch their long-standing commitment to cut net migration – the difference between the number of people entering and leaving the country – to below 100,000, after repeatedly failing to meet it.