The members say they'll continue as a four-piece after Zayn Malik announced he was leaving the group last week to "live like a normal 22-year-old".
His departure was followed by rumours on Twitter, Instagram and Facebook that One Direction was about to break up.
But Liam Payne thanked fans for sticking with the band and for "not thinking it's finished".
He tweeted: "I can see a lot of people thanking us for staying but your the real Heros here thanks for not thinking it's finished."
The band continued their On the Road Again tour and have been playing concerts in South Africa.
They start the European leg of the tour by playing Cardiff's Millennium Stadium on 5 and 6 June.
Zayn Malik quit the group last week after flying back to the UK, having been "signed off with stress".
It was after reports that he'd cheated on his 21-year-old fiancee, Perrie Edwards.
He told The Sun that he was "upset" for the group's fans and he said there was no bad blood between him and his former bandmates, who he said had been "really supportive".
It's thought he's working on a solo album with producer Naughty Boy, who's worked on tracks for Emeli Sande, Cheryl Cole and Leona Lewis.
Follow @BBCNewsbeat on Twitter, BBCNewsbeat on Instagram and Radio1Newsbeat on YouTube

The 27-year-old has made 73 appearances for Blues since joining in 2013 but spent the past 18 months out on loan.
Last season, the once-capped Scotland international helped Hibernian win promotion to the Scottish Premiership, scoring three goals in 32 games.
"To get him for Luton is a real coup for the football club," Hatters boss Nathan Jones told the club website.
"We lost a wonderful player in Cameron McGeehan [to Barnsley] and what he does is difficult to replace, but we have brought in a different Championship-quality player and we are delighted."
Find all the latest football transfers on our dedicated page.

Owen and Karl Oyston sued fan David Ragozzino for Â£150,000 over a post on website Another View From the Tower.
The 32-year-old said he had "limited financial means" and feared what would happen should the Oystons win the case.
The judge at Manchester Civil Justice Centre gave him 21 days to respond to the claim.
The application to default hearing was brought by the Oystons on the grounds Mr Ragozzino had failed to file a defence in time to their action.
He was supported at the court by dozens of Blackpool fans, who carried banners that criticised the Oystons' running of the club.
On Friday, fellow fan Stephen Sharpe apologised to the Oystons over his online comments, withdrawing his posts after accepting they were "false, defamatory and, in some cases, threatening".
On Saturday, about 1,000 fans staged a demonstration before the club's home game with Brighton, calling for the Oystons to relinquish control of the club.

Ece Heper, 50, was arrested on 30 December in the north-eastern town of Kars, her lawyer Sertac Celikkaleli told The Canadian Press.
Canadian officials say they are offering consular assistance, but released no further information.
Turkey's penal code states that anybody who insults the president can face up to four years in prison.
Ms Heper's friend Emrah Bayram told the BBC she was arrested for Facebook posts critical of President Recep Tayyip Erdogan.
"It's ridiculous, she's expressing her opinion," he said.
Friends say Ms Heper, who lived in Ontario and is reportedly a Canadian-Turkish citizen, has "some health issues" and they are worried about her access to medication while in detention.
Along with her lawyer, they fear it could be at least a month before her case goes to trial. They have contacted human rights organisations over her case.
Mr Erdogan has been accused of mounting a growing crackdown on freedom of speech.
Almost 2,000 cases for insulting Mr Erdogan have been opened in recent years.
They include a former Miss Turkey and a 16-year-old student.
Another man was found guilty of insulting the president and given a suspended one-year jail sentence after he shared images comparing Mr Erdogan to the fictional character Gollum.
One Direction is not on the verge of splitting up, despite rumours started on social media.
[NEXT_CONCEPT]
League Two side Luton Town have signed midfielder Andrew Shinnie on a season-long loan from Birmingham City.
[NEXT_CONCEPT]
A Blackpool football fan who is accused of libelling the club's owners on the internet has told a court he has "never written anything defamatory".
[NEXT_CONCEPT]
A Canadian dual national has reportedly been detained in Turkey for allegedly insulting the country's president.