Labour has confirmed that it could accept a quota of migrants from the EU under a returns agreement it hopes to strike with the bloc if it wins power at the next election.
Shadow Cabinet Office minister Nick Thomas-Symonds said the "objective" was to secure a returns agreement to establish "management and control of the system" as he accused the Conservatives of having "lost control of our borders".
Mr Thomas-Symonds spoke to Sky News while Sir Keir Starmer and shadow home secretary Yvette Cooper meet European officials in The Hague - and as the party unveils proposals to treat smuggling gangs "on a par" with terrorists.
The potential for a returns agreement has already attracted controversy, with Tory Party chair Greg Hands accusing the party of a "shocking open door policy on immigration".
The EU is currently working on a new returns agreement that would mean each member state takes a minimum annual quota of 30,000 migrants, or pay €20,000 (£17,200) for each person they do not accept.
Mr Thomas-Symonds told Sky News: "What we are looking to do as an objective is a returns agreement.
"At the moment the government is in a position to return people already to particular countries. They are not fast tracking that situation. They're not doing that competently.
"What we would be looking for is management and control of the system, which is absolutely vital and not there at the moment under this government."
When it was put to him on Sky News that the UK is 13% of Europe's population and therefore could have to accept the same percentage of migrants under an agreement - equating to around 182,000 people per year - Mr Thomas-Symonds said he did not accept the figure.
He said the exact details would be for a potential future Labour government to negotiate with the EU.
"Our position is that net migration has been too high in the UK and we want to see that coming down. That's our overall position and that's something we'd obviously take into any negotiation with the EU," he said.
Labour also wants to have more UK police officers posted with the organisation for joint investigations - aiming to disrupt the gangs before they reach the coast - and work with EU partners on data and intelligence sharing, replacing access the UK lost to certain programmes after Brexit.
Rishi Sunak hit back at Labour's assertion that the government has "lost control of the borders" and claimed Sir Keir's plan would see the UK accept 100,000 migrants from the EU every year - although he did not say how he had calculated this figure.
Speaking to broadcasters on a visit to Devon, the prime minister said the Labour leader "spent all of this year voting against our stop the boats bill, the toughest legislation that any government has passed to tackle illegal migration".
He added: "I don't think it's credible that he really wants to grip this problem."
In August, the Times reported that Mr Sunak was also attempting to secure a returns agreement with the EU, but that the negotiations stalled.
It is likely that any agreement would have involved UK taking a share of EU migration.
In his interview with The Times, the Labour leader said he would treat people smugglers like terrorists by freezing their assets and restricting their movements.
Speaking from The Hague, Sir Keir told broadcasters: "The government has lost control of our borders, and we can see that with the number of crossings there are across the Channel in small boats. We have to stop that."
He said the "only way to do that is to smash the gangs that are running this vile trade," and that he had been speaking to Europol today about getting a "closer agreement" to tackle it.
"That is taking control of a situation that the government has totally lost control of," he declared.
Sir Keir rejected assertions that such a deal with Europe would be a betrayal of the 2016 Brexit referendum, and said the only way to defeat the gangs is to "operate where they're operating", which is in Europe and beyond.
Asked about Suella Braverman's claim that his plan would make Britain Europe's "dumping ground" for "millions" of illegal migrants, Sir Keir said it's "embarrassing that the government is pumping out this nonsense".
"I can only assume it's because they've got nothing sensible to say on this issue," he said.
More than 23,000 people have made the dangerous journey across the Channel in the year so far - with more than 3,000 making the crossing in September alone.
Prime Minister Rishi Sunak has made tackling the issue one of his five priorities for the year, promising to "stop the boats" with measures such as deporting some migrants to Rwanda and housing people on barges.
But both schemes have hit barriers, with Rwanda flights caught up in the courts and an outbreak of Legionella disease on the Bibby Stockholm vessel.
Mr Sunak has repeatedly defended the government's progress, saying: "We've already reduced the legacy backlog by over 28,000 - nearly a third - since the start of December and we remain on track to meet our target."