Theresa May has admitted that bringing down net migration to the Tory target of below 100,000 will "take some time" as Downing Street refused to put a deadline on reaching the goal.
The Prime Minister insisted she was committed to reducing the number of people coming to the UK to "sustainable" levels, which meant the "tens of thousands".
She said that one of the key messages from the Brexit vote was the importance of having "some control" over the movement of people from the EU into the UK.
At a press conference with German chancellor Angela Merkel in Berlin, she said: "I've always been clear that the reason that we looked to set a number in relation to net migration is because we want to bring net migration into the UK down to sustainable levels.
"Sustainable levels is, we believe, in the tens of thousands. Now, it may take some time to get there."
She added: "One of the messages from the Brexit vote was the importance of bringing some control into the movement of people from the European Union into the UK. So that's another factor we will be looking at in relation to looking at the net migration for the future.
"But it's about sustainable levels and I believe those sustainable levels are in the tens of thousands."
Earlier, Mrs May had been challenged about the target during her first Prime Minister's Questions appearance in the Commons.
She said: "I am very clear that the vote that was taken in this country on June 23 sent a very clear message about immigration; that people want control of free movement from the European Union and that is precisely what we will be doing and ensuring that we get in the negotiations that we will be undertaking."
A Downing Street source said that the PM was "absolutely committed to making sure she gets immigration down to a sustainable level. In her view that is tens of thousands."
Asked whether Mrs May was dropping a target of 2020 to reach that goal, a senior source said: "The manifesto stands."
The Conservative manifesto for the 2015 election states that the Tories would "keep our ambition of delivering annual net migration in the tens of thousands" and adds: "That ambition remains the right one.
"But it is clearly going to take more time, more work and more difficult long-term decisions to achieve. Continuing this vital work will be our priority over the next five years."
A Number 10 spokesman later told reporters: "It remains a priority for this Government to get immigration down to sustainable levels, which is in the tens of thousands. That's a priority throughout the term of this Government.
"We are not putting a timeframe on that."