UN Secretary General Ban Ki-Moon has been among those calling for a postponement of next Monday's elections.
They are to be followed by presidential elections in July in which president Pierre Nkurunziza is seeking a third term contrary to the constitution which has a limit of two terms.
The protest against him are from his own Hutu group so it has not developed into an ethnic clash between Hutus and Tutsis.
But Helen Clark, now head of the UN Development Programme, noted the coincidence in timing of New Zealand assuming the chair: in 1994 it chaired the Security Council during the genocide by Hutus in Burundi's neighbour Rwanda when 800,000 people were slaughtered in about 100 days.
"It's sad in a way that it is 21 years since New Zealand chaired [the Security Council] during the Rwanda crisis which was genocide and here we are with the Great Lakes region.
"I'm not suggesting genocide but there's the possibility of quite serious events."
Helen Clark is back in New Zealand briefly to attend a regional humanitarian conference in Auckland and was in Wellington briefly last night to launch a book by her long-serving former chief press secretary Mike Munro.
Commenting on a plan by Foreign Minister Murray McCully to involve the Security Council in getting Israeli and Palestinian leaders back the negotiating table in the next six months, she said it would be good to see some fresh diplomacy on the issue.
"[US Secretary of State] John Kerry tried very hard but in the end there was a gap that wasn't able to be bridged. I think people would welcome the Security Council under New Zealand chairmanship having a fresh go at it."
On Andrew Little's leadership and the proposals to let Australian charities provide social housing in New Zealand:
I'm not really watching New Zealand politics closely at all. My main source is my father who tells me what is going on on the TV news. If that sparks sufficient interest, I may even go into Herald website from time to time.
If I start commenting down those lines [social housing] I'll be right back into partisan politics. I don't think that's where I want to be right now.
On when she might signal whether she wants the UN Secretary-General job or not:
Well it is still relatively early days. The Secretary-General is three and half years into a five-year term and normally the issue wouldn't be resolved until well into the fifth year so let's say there's a lot of shadow boxing at the moment.
On UN development programme work in the Middle East:
The Syria crisis is the big pre-occupation. We have been involved with the Syria response plan and then what's called a regional Refugee and Resilience Plan.
At the end of March I went to Kuwait City where the pledging conference around these plans was. So what do we do?
Several things: Working in Syria itself on basic livelihoods for people. The economy is wrecked as you can imagine so trying to support people to be able to keep baking the bread, and sewing clothes and clearing away the debris from the bombing, water from the small farms, basic services, we raise what we can for that work.
We estimate that last year we probably had a positive impact for about 2.3 million people, so it is not a small number.
We have also been involved in supporting countries round about and Lebanon and Jordan are particularly needy because they are very small countries with the equivalent of about 25 per cent of their countries being refugees.
It is a huge strain. Ask ourselves as New Zealanders of 4.3 million, had a million guests turned up, how would we feel? This is what Lebanon is facing in a pocket handkerchief-sized country, and Jordan has pretty similar numbers.
In the end we've had to get involved with basic livelihood work for the locals as well as the newcomers, supporting municipalities with services - there's not enough water, there's not enough electricity - and working with local leaders to try to keep some atmosphere of tolerance.
When you look at the numbers, you have to say to full credit to these societies that they have not imploded under the strain of a quarter of their population turning up.
I was also in Turkey at the end of April, around the time of Gallipoli and I went down to the border with Syria where some of the refugee camps are.
Turkey has around two million refugees - about 1.75 million of them are Syrian and the others are Iraqis. Turkey has been very good at providing camps and support but the strain is telling.
When you've had people there for up to four years and no sign of being able to go home and Turkey has been paying for everything, yes it is a strain.
The kind of support we get involved in there is working through municipalities, job creation, to try and cushion the burden.
On UNDP's role in trying to prevent such crises:
It could be a case of "none so deaf as those that do not want to hear" because what you can observe is that when you have significant political exclusion, often compounded by economic and social exclusion, at some point the dam will burst and you will get an uprising.
The issue is whether there is leadership that is smelling the coffee around that.
What we have seen in several of the Arab states is a willingness to reform. You saw that in Morocco. You've seen it in Jordan itself in a move to greater democracy.
But where people try to keep a very tight grip on power and there's others wanting a share of the action, there will be trouble.
On a new set of sustainable development goals:
There is this 'Goal 16' in the new Sustainable Development Goals which talks about peaceful inclusive societies characterised by access to justice and responsive and inclusive institutions at all levels - which is code for saying that for development to be sustainable, people have got to feel that things are fair.
If they don't think things are fair, you have the basis for grievance, which, in extremis, can tip societies right over and, tragically, we see quite a lot of that.
