Rishi Sunak has suggested he could fail to meet his pledge to “stop the boats” by the next general election.
The prime minister has made cracking down on asylum seekers crossing the Channel one of his top five promises to voters.
Asked on Monday if he would meet the target before voters go to the polls, Sunak refused to say yes.
“I want it to be done as soon as possible but I also want to be honest with people that it is a complex problem,” he said.
“There is not one simple solution and that it can’t be solved overnight and I wouldn’t be being straight with people if I said that was possible.”
Sunak said the current situation was “unsustainable and is completely unfair” on taxpayers who were paying to house migrants.
“That’s not right. We’ve got to put a stop to that. And we’re working on it,” he said.
“It’s not an easy problem to fix,” he added. “It will take time and we have to attack it from lots of different ways.”
The next election must be held by January 2025 at the very latest, with polls suggesting Labour are on course to win.
Downing Street launched a media blitz at the start of August to highlight government plans to prevent people crossing the channel.
But so-called “small boats week” backfired after six people died attempting to cross from France to the UK on Saturday when their boat sank.
And all 39 people being housed on the Bibby Stockholm barge in Dorset were removed after the Legionella bacteria was discovered on-board.