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The 47-year-old was found dead in her luxury Sydney flat on Saturday.
Ms Dawson had long battled depression and she was outspoken against social network bullying, which she said she was a victim of.
Mr Key told TVNZ's Breakfast today he had met her on a number of occasions.
"She was, I thought a really lovely person and it was tragic news on the weekend.
"I was very sad to hear the news."
He acknowledged New Zealand had a cyber bullying problem and there was legislation going through Parliament targeting it.
"I don't actually myself think New Zealand is any worse than any other country - I'd be absolutely amazed if it was."
But it would be very difficult to eradicate social network attacks completely, Mr Key said.
"In the end the internet is such a free and open place where people put up whatever they feel like, and you get an enormous amount of information pouring into the internet and therefore out for people to see and a lot of it can be quite awful."
Ms Dawson had earlier told the Herald on Sunday her native country was "small, nasty and vindictive".
Things were no better for her in Australia, where she was viciously attacked. "Twitter trolls" taunted her and told her she should kill herself.
Dawson was rushed to St Vincent's Hospital in Sydney in September 2012 after an apparent suicide attempt.
- Lifeline - 0800 543 354
- Depression Helpline (8 am to 12 midnight) - 0800 111 757
- Healthline - 0800 611 116
- Samaritans - 0800 726 666 (for callers from the Lower North Island, Christchurch and West Coast) or 0800 211 211 / (04) 473 9739 (for callers from all other regions)
- Suicide Crisis Helpline (aimed at those in distress, or those who are concerned about the wellbeing of someone else) - 0508 828 865 (0508 TAUTOKO)
- Youthline - 0800 376 633, free text 234 or email firstname.lastname@example.org
- What's Up (for 5-18 year olds; 1 pm to 11 pm) - 0800 942 8787
- Kidsline (aimed at children up to 14 years of age; 4 pm to 6 pm weekdays) - 0800 54 37 54 (0800 kidsline)