By early afternoon many would-be investors were experiencing difficulty getting on to the site.
Staff at the share offer's call centre advised trying again "in a few hours''.
Some users who were able to access the site reported difficulties in completing the pre-registration.
Speaking from Mexico overnight where he is having trade talks, Mr Key said he understood issues with the website crashing were now resolved.
"There's been a very significant number of registrations in the first 24 hours, an indication of how popular the interest is in terms of finding out what's going on. That's a good sign."
Asked if there was a concern the Government guarantee of at least $2,000 in shares for New Zealanders who wanted to invest risked pushing the share price up, he said he had to be careful what he said with the process underway.
However, asked if there had been more interest than anticipated, he said "it's certainly been very significant".
"We are absolutely going to honour the commitments we have made which is for New Zealanders to be at the front of the queue, so if there is lots of retail interest, then there will be lots of New Zealanders at the front of the queue. We'll accommodate all of that."
Mr Ryall said on Monday that the Government was "pretty confident that the website will be able to deal with a wide range of traffic".
But by late yesterday he acknowledged that "huge volumes of traffic on the website in the first few hours" were causing problems.
"Some people may have had difficulty accessing the site, and others will have noticed it was slow in processing requests for information."
By 8pm about 70,000 New Zealanders had pre-registered, with about five per second at times, he said.
The National Party said that figure had risen to 100,000 by 8:30am today.
"There is plenty of time before pre-registration ends on 22 March - and there is no advantage in pre-registering earlier."
But at least some would-be investors were able to pre-register before yesterday. One Auckland woman told the Herald she was able to pre-register on Monday evening by following a link contained in an emailed newsletter from National's Hunua MP, Paul Hutchinson.
The Government's $1.1 million advertising campaign for the share offer also began last night with taxpayer-funded ads on television and Trade Me. The ads had been vetted by the Auditor General to ensure they did not include political messages.
Despite strong public opposition to the Government's partial asset sales, Labour's SOE spokesman, Clayton Cosgrove, said early indications of keen public demand for shares were "eminently predictable".
"It is very similar to Contact Energy - I think you had 220,000 Kiwi shareholders initially - and today that company is now foreign-owned and the National Government lost an election over it so it doesn't surprise me at all."