Telecom says an internet security glitch that prevented Yahoo! Xtra email account holders from changing their passwords has been fixed.
Five percent of Telecom's 450,000 Yahoo! Xtra accounts were corrupted in the latest attack last weekend, where hackers sent infected messages to third parties.
Telecom had earlier advised that customers who fail to change their passwords by the end of Friday would be locked out of their accounts until they did so.
Technology commentator Ben Gracewood said on Friday the best way for Telecom to solve its problems with cyber attacks is to change its email provider.
Mr Gracewood says while changing passwords regularly is important, it makes no difference in this case.
"The way the hack was executed, it's kind of irrelevant what your password was - it was simply if you had been logged on at some time. Because of the compromise to Yahoo! ... if you went and visited the wrong site they had access to your email."
Mr Gracewood says Telecom needs to put more pressure on its providers to apply patches and follow protocols to avoid falling prey to cyber attacks.
However, Telecom says Yahoo! has assured it that customers who have changed their passwords this week are no longer sending spam.