The Ulster Unionist Party leader had earlier said he was “on the cusp” of quitting amid controversy over the tweets.
Mr Beattie has faced accusations of misogyny and racism over the content of tweets posted before he entered political life.
“I apologised for what I had done directly to each one of them and then I spoke (about) whether or not I still had their support to remain as party leader – overwhelmingly every one of them said ‘yes, I did’.
“So I have support from my MLAs.
“But I also spoke with party officers and the party chairman about party officers who also had a discussion around the issue and I have support also from party officers.”
Mr Beattie said the support was “unanimous”.
He said conversations would continue with other UUP members over the historical tweets.
Meanwhile, DUP minister Edwin Poots and his wife Glynis have issued defamation proceedings against Mr Beattie after he tweeted a joke about her that referenced a brothel.
Proceedings have also been initiated against Conservative MP and chair of Westminster’s Northern Ireland Affairs Committee Simon Hoare, who retweeted Mr Beattie’s joke.
Patrick Higgins, from Donnelly and Wall solicitors in Belfast, told the PA news agency that letters had been sent to both men seeking remedies for their actions.
“Today we instigated proceedings on behalf of Mrs and Mr Poots against Mr Beattie MLA and Mr Hoare MP, who published this tweet,” he said.
“This post constitutes a grave and unwarranted attack on my clients’ reputation.
“As a couple of 36 years, married for 33, it has caused my clients profound distress.
“As a lady who has recently retired after dedicating her life as a nurse to caring for terminally ill children, it is wholly inappropriate for any persons to make such comments and the publication has caused immense hurt to her, her husband and their family.”
Doug Beattie had earlier said he offered to resign on Monday but close colleagues in the party urged him to take the time to consider his future.
The Upper Bann MLA conceded that the posts, the majority of which were written around a decade ago, were “horrendous and horrific”.
The furore erupted on Saturday evening when Mr Beattie tweeted a joke that referred to the wife of political rival Edwin Poots and a brothel.
Mr Poots, DUP Stormont minister, said his wife was “disgusted” by the post, which Mr Beattie deleted and apologised for.
He reiterated that apology on the floor on the Assembly on Monday, insisting he was “truly sorry”.
The controversy escalated after focus turned to Mr Beattie’s historical conduct on Twitter, with a series of derogatory remarks about women, Muslims, members of the Travelling community, and people with mental health issues unearthed.
The dramatic turn in fortunes for Mr Beattie came just hours after a newspaper opinion poll indicated he is the most popular political leader in Northern Ireland.
Mr Beattie said his confidence has been rocked by the controversy and he has isolated himself from friends and loved ones.
“I have to pick myself up and come out of the shadows and face this head-on,” he said.