He later posted a message on his page thanking people for alerting him to the recent hacking of his account.
"Passwords reset and security investigation now under way," he said.
"Obviously we've regained control of our Twitter account - I don't want to be having to do that every afternoon."
Mr Craig said he would not make such a comment.
"It's not something I would say and I don't think anyone should put words in anyone else's mouth."
"I doubt that it's true anyway. I think it's despicable when people stoop to these sorts of means to discredit people - I know it goes on, I know Twitter is vulnerable but obviously until now we've avoiding being hacked."
The Conservative Party's email and website had been hacked in the past, according to Mr Craig.
He believed today's tweet was aimed to "discredit and misinform".
Conservative Party press secretary Rachel MacGregor posted a message on her Twitter account calling for a "Twitter expert for some paid work urgently... know anyone who knows about how people hack into twitter accounts and how to best stop it".
Mr Craig said he was looking forward to Twitter security being upgraded because it was too easy for people to hack others accounts.
In February this year Twitter reset more than 250,000 passwords after noticing unusual access patterns and hired a security engineer to develop more robust authentication.
Hackers recently compromised the Twitter account of the Associated Press, sending out a false tweet about an attack at the White House.
The tweet said there had been two explosions at the White House and that President Barack Obama was injured. The attack on AP's Twitter account and the AP mobile Twitter account was preceded by phishing attempts on AP's corporate network.
