Labour leader Jeremy Corbyn has said he stands by his view that immigration to the UK from the EU is not too high.
He told the BBC's Laura Kuenssberg migrants played a valuable role and he was not proposing new restrictions on the rights of people to come to the UK.
Mr Corbyn said Labour was not "wedded" to freedom of movement, but denied this represented any change of stance on his part.
The Conservatives accused Labour of being "in chaos" over immigration.
Mr Corbyn gave several media interviews ahead of a much-publicised speech on Brexit, discussing the issue of whether freedom of movement of EU citizens should persist once the UK leaves.
In his speech, in Peterborough, Mr Corbyn said he supported "fair rules" and "reasonable management" of immigration after Brexit but said that must be set against continued access to markets for British business.
"Labour is not wedded to freedom of movement for EU citizens as a point of principle, but I don't want that to be misinterpreted, nor do we rule it out," he said.
"We cannot afford to lose full access to the European markets on which so many British businesses and jobs depend.
"Changes to the way migration rules operate from the EU will be part of the negotiations."
Talking to the BBC's political editor, Mr Corbyn, who has repeatedly insisted since becoming leader that EU migration to the UK is not too high, was asked if the speech meant he had now changed his view.
He replied: "No. My mind is quite clear that we need to end the exploitation that's going on, we need to maintain a market access within Europe and we need to ensure there are good relations between all communities."
Mr Corbyn said the focus should be on ending the abuse of low-skilled workers under existing EU employment rules and promoting more local recruitment - which he argued would "probably" reduce immigration, irrespective of Brexit.
Analysis by Laura Kuenssberg, BBC political editor
Despite the impression given by Labour HQ overnight that Jeremy Corbyn was on the point of ditching his long-held backing of the freedom of movement of European citizens - that allows an unlimited number of them to come and live and work in the UK - when push came to shove in interviews this morning, he couldn't quite bring himself to say it.
He has not changed his mind on the most basic question when it comes to immigration. Does he think that the current levels, with 190,000 EU citizens coming to the UK last year, are too high? "No."
For many of his supporters, that might be a relief. He has continually defended the rights of people to come to the UK and refused to put a limit on numbers.
But for the increasing number of Labour MPs who have come to believe that the public demands a very different approach, it is a problem.
Asked whether he agreed that anyone without a job offer should be barred from coming to the UK, he said: "We are not saying that anyone could not come here because there would be the right of travel and so on.
"The right to work here would be something that would have to be negotiated."
The Labour leader said the "grotesque exploitation" of EU migrants by some UK companies had caused "awful tensions" in communities because of the under-cutting of wages.
But he defended the role of migrants in helping the NHS and other public services function.
While the UK was definitely leaving the EU, he said it could not "avoid" having a close trading relationship with the continent.
"What we don't want to do is turn Britain into a bargain-basement economy on the shores of Europe where we continuously reduce corporation taxation, encourage a low-wage economy," he said.
"Instead what we want is a high-value economy with skilled jobs promoting high-quality exports."
On Sunday, Theresa May told Sky News it would not be possible to hold on to "bits" of EU membership after Brexit, leading to widespread reporting that she was moving towards leaving the European single market, with restricting immigration a priority.
A Conservative spokesman said it was clear Mr Corbyn would not impose any controls on immigration.
"First he said Labour wasn't wedded to freedom of movement, now he says that there are circumstances in which he could keep it," he said.
Liberal Democrat leader Tim Farron said his Labour counterpart was "still no clearer" on immigration.
He added: "He failed to pull a shift to keep us in the EU before the referendum and now he is helping Theresa May, [International Trade Secretary] Liam Fox and [Foreign Secretary] Boris Johnson yank us out of the single market."
UKIP said working families would not be fooled by what they said was a "load of flannel".
In his speech, Mr Corbyn also called for curbs on boardroom pay but appeared to back away from his support earlier in the day for a maximum wage.
He told Radio 4 he would personally support a cap on earnings as part of his vision of a more equal country but later said he favoured controlling pay ratios to limit the amount that bosses could earn in relation to their workers.