Stampeding elephant kills man on honeymoon.
It is thought that the couple were on foot with an escort around 300 metres from a luxury encampment when the elephant struck.
It was not initially clear whether the elephant had been startled or whether it had been a 'rogue' animal. It was also unclear whether it had been part of a herd, or was on its own.
Kenya Wildlife Service spokeswoman Connie Maina said that efforts would be made to track the animal to determine what had happened.
It is understood that Mr Smith worked in the IT department at Reuters. His wife is also an employee of the company.
A spokesman for Reuters said, 'Clearly it is a very tragic situation, we are sending our condolences to the family, we are trying to help them practically as best we can.'
Ms Maina said that the couple had been a short distance from Richard's Camp, an upmarket encampment on the edge of a small forest in an area known for elephants.
She said it was possible that the elephant had been startled.
'It is very unusual ... but accidents can happen,' she said.
'It is very unfortunate.'
She continued, 'They say it was one elephant, I'm trying to find out whether it was a lone bull.'
She added that the Kenya Wildlife Service would monitor elephants in the area to determine if there was a rogue animal at large.
'We will try to monitor to see if we can get any leads, if it is a rogue elephant it may do this again, but we don't have any information on whether it is or not.'
She added that the tragedy had shocked wardens in the reserve.
'Everyone is feeling it,' she said.
Jake Grieves-Cook, chairman of the Kenya Tourist Board, said that he understood a herd of elephants had been startled by something and charged the couple, killing Mr Smith and knocking over the guide.
'No-one knows what startled the elephants, but the guide was doing everything right,' he said.
'They were downwind and thought they were a safe distance. Elephants have very poor eyesight so this was not an attack.
'It was a tragic accident.'
A Foreign Office spokeswoman confirmed Mr Smith's identity and said that consular assistance was being offered to the family. Reports said that Mr Smith's body had been flown from a nearby landing strip to Nairobi. It is understood that other family members were flying out to be with Mrs Smith.