Theresa May said that Britons sent a "very clear" message pushing for the country to take back control of its borders when they voted for Brexit.
Her comments at a meeting with the German chancellor Angela Merkel are likely to add to tension over the terms of the UK's exit from the EU.
Ms May must square her commitment to curb immigration with the economic need for free access to the bloc's markets.
Europe has made it clear that Britain cannot have free trade without free movement - and that is likely to prove a sticking point in any talks.
Theresa May has insisted that Brexit will not mean "walking away from our European friends" as she embarked on her first foreign trip since being made prime minister.
Ms May, appearing alongside German chancellor Angela Merkel in Berlin, insisted that the UK would remain an "outward-looking country" after the European Union referendum result.
I have been clear that Brexit means Brexit and the United Kingdom is going to make a success of it.
But I also want to be clear here today, and across Europe in the weeks ahead, that we are not walking away from our European friends.
Britain will remain an outward-looking country and Germany will remain a vital partner and a special friend for us.
Theresa may have brushed up on her German skills for her first foreign trip since being made prime minister a week ago.
She greeted the German chancellor Angela Merkel in her own language as they hosted a joint press conference today.
"I am delighted to be in Berlin" she said in German, hastily adding: "I will now go into English".
Her efforts seems to have made a good early impression on Ms Merkel as the pair got to know each other at their first meeting.
The chancellor appeared visibly surprised and pleased at the gesture.
Theresa May has landed in Berlin for talks with the German chancellor Angela Merkel on issues including Britain’s exit from the EU.
It marks Ms May’s first foreign trip since she took over as prime minister earlier this month.
She was welcomed with a full guard of honour at the airport, where she shook hands with Ms Merkel.
Ms May is expected to stress that the UK is in no hurry to leave the EU and also sound out the German leader over possible terms of a Brexit.
However, German officials have said there can be no official “pre-negotiations” before the UK triggers article 50 to leave the bloc.
Theresa May displayed "an incredibly calm authority" during her first Prime Minister's Questions, the assistant editor of the Spectator magazine has told ITV News.
Isabel Hardman said she was "surprised" by Mrs May's performance, saying she had expected her to be "quite dull".
She said although Mrs May did not have David Cameron's "swagger", she fitted her jokes in well.
But Ms Hardman warned there will be tougher tests ahead at the dispatch box.
"When she does eventually lose her temper that will tell us a lot about Theresa May," she said.
Theresa May launched a series of scathing attacks on Jeremy Corbyn during her first appearance at Prime Minister's Questions.Read the full story ›
Theresa May has moved to temper expectations for the Government to hit its immigration target.
The prime minister suggested attempts to meet the target could be hit by Brits moving back from the EU and that it may take some time to hit the target.
Immigration target (still tens of thousands) could be hit by Brits moving back from EU - suggests @theresamay
Asked whether immigration will be brought down to the tens of thousands? 'It will take some time to get there' says May
Jeremy Corbyn was mocked by one of his own MPs during PMQs for his stance on the UK's Trident nuclear deterrent.
Mr Corbyn opposed a motion to renew the deterrent earlier this week, earning him strong criticism from many in his own party.
Today, Labour MP Jamie Reed thanked Theresa May for her "wholehearted support and endorsement for official Labour Party policy on Trident".
"It's such a refreshing change to hear that from the dispatch box," he said as Mr Corbyn sat stony-faced on the front bench.
Theresa May has been widely praised for her debut at Prime Minister's Questions.
Best PMQs debut by a PM. Better than Blair, Brown & Cameron. A measure of her experience & composure & the quality of her opponent.
Impressive #PMQs debut from Theresa May, from remembering MPs' birthdays to utterly filleting Jeremy Corbyn. She may be around for a while.