Widely reported claims about Labour's immigration plans have been dismissed by the party, who said they reflected ideas in a discussion paper and were not official policy.
So what are the main parties promising on immigration in their manifestos?
The Conservative manifesto promises to cut net migration below 100,000 a year. The party says it would "reduce and control immigration" while ensuring that businesses can recruit "the best and brightest" from around the world and universities can attract overseas students.
Theresa May's party would double to £2,000 a year the Immigration Skills Charge on companies employing migrant workers, with revenues invested in skills training for UK workers. The Immigration Health Surcharge would rise to £600 for migrant workers and £450 for international students, to cover their use of the NHS.
The earnings threshold for people wishing to sponsor migrants for family visas will be increased. Visa requirements for students will be tightened and they will be required to leave the country at the end of their course, unless they meet new thresholds. Overseas students will continue to be included in migration statistics.
The independent Migration Advisory Committee will be asked to make recommendations for changes to the visa system expected to allow "significant" numbers of visas for workers in key sectors without adding to net migration as a whole.
Labour promises "fair rules and reasonable management of migration" and rejects "bogus" immigration targets. The party pledges not to scapegoat migrants, discriminate between people of different race or creed or blame them for economic failures.
A new migration system will be based on the UK's economic needs, identifying specific labour and skill shortages in consultation with business and unions. A Labour administration would take action to end exploitation of migrant workers, stop overseas-only recruitment packages and increase prosecutions for paying below the minimum wage.
Labour would reinstate a Migrant Impact Fund to mitigate strains on public services in areas with high numbers of incomers. It would remove international students from immigration statistics.
Income thresholds for visas would be replaced by a ban on accessing public funds. Indefinite detention of migrants would be ended. Britain would take in its "fair share" of refugees.
Liberal Democrats will "make the positive case for immigration", which their manifesto describes as "essential to our economy and a benefit to our society". It promises to ensure the immigration system works "fairly and efficiently".
Tim Farron's party would stage an annual parliamentary debate to identify the migration needed to meet labour and skill shortfalls. It would allow high-skilled immigration, remove students from migration statistics and reinstate post-study work visas for some overseas graduates.
A centrally-funded Migration Impact Fund would help local communities adjust to migration and there would be additional government funding for English lessons for new arrivals.
Britain would continue to "uphold our responsibilities" to assist refugees, offering safe and legal routes to the UK for refugees. Some 50,000 vulnerable people would be admitted from Syria over five years and the Dubs Scheme would be reopened to take in 3,000 unaccompanied child refugees. A new limit of 28 days would be placed on immigration detention. Asylum would be offered on the basis of sexual orientation or gender identification.
SCOTTISH NATIONAL PARTY:
The SNP manifesto "encourages the best and brightest from Europe, and around the world, to make Scotland their home". It promises to "stand firm against the demonisation of migrants".
The party will press for immigration powers to be devolved to the Scottish Parliament, so that Scotland can offer different arrangements from the rest of the UK to attract European nationals. And it will make the case for the reintroduction of a Post-Study Work Visa scheme for Scotland to allow overseas graduates to remain.
The SNP will push for the abolition of the Skills Immigration Charge and oppose its extension to EU nationals. The party calls for a 28-day limit on immigration detention and opposes the detention of children, pregnant women and people with mental illness.