Labour is promising to cut net migration to the UK if it wins the election next month, but will not set an overall target.
Shadow home secretary Yvette Cooper said her party would reduce the need for overseas workers by improving training of British workers.
She argued that not setting a target was “sensible” because the Conservatives had “discredited the whole system” by previously missing targets.
But the Tories said “no-one believes Keir Starmer is serious about tackling immigration”.
Speaking on BBC One’s Sunday with Laura Kuenssberg, Ms Cooper acknowledged that new salary levels announced by the government were yet to “play through” and would further restrict companies’ access to work visas.
But she added that Labour wanted to go further to cut reliance on foreign workers in sectors including construction, IT, social care, health and engineering.
The party says if it wins power, it will pass a new law to force different parts of the government to draw up skills improvement plans in high-migration sectors. It is not yet clear how these plans would be enforced.
Ms Cooper said Labour wanted to see “significant changes in place” across the economy to reduce reliance on overseas workers.
But she added the party would not set a migration target because the Conservatives had “ended up being totally all over the place” when they did.
She also argued that other factors would produce variations “from one year to another,” citing the pandemic and the UK’s decision to accept Ukrainian refugees as recent examples.
Leader Sir Keir Starmer told the Sun on Sunday: “Mark my words, a future Labour government will bring down net migration.”
Last year, net migration – the number of people coming to the UK, minus the number leaving – was 685,000, figures from the Office for National Statistics (ONS) show.
Earlier this year, the government introduced new laws designed to cut immigration numbers.
They included increasing the minimum salary requirement for some skilled work visas by nearly 50%, as well as increasing the salary requirement for skilled workers to bring family dependents with them.
Ms Cooper said Labour supported those changes, acknowledging they would “lead to further restrictions on visas”.
Labour also wants to lengthen the bans on hiring foreign workers that can be handed down to firms that breach employment law, such as by paying below the minimum wage.
A spokesperson for the Conservative Party said the Labour policy announced on Sunday was a “U-turn” on Sir Keir’s principles.
“This is the man who called all immigration laws racist and voted against tougher border controls 139 times,” the spokesperson said.
That refers to a book review Sir Keir wrote when he was a lawyer in the late 1980s, in which he said the author had highlighted the “racist undercurrent which permeates all immigration law”.
Alison Thewliss, from the SNP, said: “Instead of coming forward with policies based on Scotland’s needs, Keir Starmer and Rishi Sunak are both amping up the far-right belief that migrants are to blame for all of our problems – but it’s not migrants, it’s Westminster.”
“From our care sector and our NHS to our economy, the cruel immigration policies that both the Tories and Keir Starmer’s Labour have now adopted directly harm Scotland,” she said.
A spokesperson for the Liberal Democrats said: “It’s clear the Conservatives have failed on immigration and broken every promise they’ve ever made.”
