LISBON—U.K. Prime Minister David Cameron announced on Friday that Britain will take in "thousands" of Syrian refugees, marking a major U-turn in his response to Europe's migrant crisis following a public outcry for him to do more.

"Given the scale of the crisis and the suffering of people, today I can announce that we will do more, providing resettlement for thousands more Syrian refugees," he said following a meeting with his Portuguese counterpart, adding that the government will discuss exact numbers with partners and set out more details next week.

"We will continue with our approach of taking them from the refugee camps—this provides them with a more direct and safe route to the United Kingdom rather than risking the hazardous journey which has tragically cost so many of their lives," he said.

The announcement marks a major shift for Mr. Cameron who just two days ago said taking more refugees from Syria wasn't the answer, an uncompromising stance that had put Britain at odds with Germany and other European Union allies that have said they would offer refuge to thousands fleeing war.

He reiterated that stance Thursday, saying the U.K.'s huge humanitarian commitment to the Syrian refugee crisis and deployment of navy ships to the Mediterranean showed the country cared.

But the prime minister has looked increasingly on the wrong side of the argument in recent days especially after pictures of a drowned Syrian boy washed up on a beach in Turkey triggered an outpouring of sympathy for refugees and calls for Britain to do more to help.

U.K. politicians from across the political spectrum, including from within the prime minister's centre-right Conservative Party, have urged him to do more. A public petition calling for the government to accept more asylum seekers has also garnered more than 230,000 signatures by Friday morning, exceeding the 100,000 mark that would make it eligible for consideration in a debate in parliament.

Mr. Cameron said on Thursday that Britain would fulfill its moral responsibilities and that as a father he felt deeply moved by the pictures of the dead boy on the beach.

His original uncompromising stance also potentially threatened his mission to renegotiate Britain's relationship with the EU ahead of a holding a national referendum on membership of the bloc by end of 2017. Some EU politicians indicated in recent days that the British prime minister cannot expect to get what he wants if he doesn't show solidarity on the migration crisis.

Mr. Cameron is visiting his counterparts in Lisbon and Madrid on Friday to discuss his EU reform agenda, although those talks are likely to be overshadowed by the migration issue.

German Chancellor Angela Merkel said on Thursday that she agreed with French President Franç ois Hollande that the EU needs a binding quota to distribute refugees fairly.

Britain has focused its efforts on providing humanitarian aid to help the refugee crisis in Syria and in neighboring countries such as Lebanon, Jordan, Turkey, and Iraq, committing £ 900 million since 2012 to provide food, shelter, medical care and clean drinking water to thousands of people affected by the Syrian civil war.

It has also contributed to the military effort against the militants who call themselves Islamic State in the region, joining the U.S. and other nations in a bombing campaign against the group in Iraq.

While the U.K. has provided a home for some refugees, the numbers are far lower than taken in by some other large European countries.

The U.K. has brought 216 Syrians to live in Britain under a scheme started in early 2014 to relocate people who are deemed particularly vulnerable, according to the government. Britain has also granted asylum to about 5,000 Syrians who have reached Britain since the start of 2011. A total of 11,600 people were granted asylum in the year to the end of June, according to Home Office figures.

Almost 65,000 people fled war-ridden Syria to Germany last year, marking an increase of almost 250%.

Oxfam welcomed the news that Mr. Cameron would announce more help. The Non-Government Organization said it hoped the government would clarify as soon as possible the number of Syrian refugees it planned to resettle and when.

"Offering to resettle 10,000 Syrian refugees would bring the U.K. in line with other European countries who have already shown leadership in offering a haven to vulnerable refugees," Mark Goldring, the chief executive of the NGO, said in a statement.

Write to Patricia Kowsmann at patricia.kowsmann@wsj.com and Nicholas Winning at nick.winning@wsj.com

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(END) Dow Jones Newswires

September 04, 2015 06:55 ET (10:55 GMT)