Since mid-May, Nigerian forces have been engaged in a concerted crackdown against the Islamist militant group Boko Haram, bombing their bases, raiding neighbourhoods where they are suspected to be hiding and cutting phone lines.
The remote, semi-desert region where the operation is being carried out is sparsely populated.
“There are 4 000 refugees who have come in from Nigeria and we are working out a programme with the International Red Cross to set up a refugee camp for them near the town of Mokolo,” Cameroon's Far-North region governor Fonka Awa said.
Nigeria's military was not immediately available for comment. The local Red Cross said it was still investigating.
The figure was much lower than that given by Hamed Jaha, a member of parliament in Nigeria's Borno state, who said on Monday that 20 000 had fled from the Nigerian border towns of Ashigashiya and Ngoshe into Cameroon after army raids.
Last month, the UN refugee agency said it had registered 6 000 refugees from Nigeria in neighbouring Niger.
Boko Haram has become the biggest risk to stability in Nigeria, Africa's top oil producer and second largest economy, but rights groups and aid agencies fear that the longer the offensive against it goes on, the more the local population will suffer.
A government rights watchdog said this week that violence since President Goodluck Jonathan declared a state of emergency in May had forced thousands of farmers to flee their land. It said the exodus could trigger a food crisis.
The National Human Rights Commission said it had credible reports of killings, torture, rape and arbitrary detention by security forces. Nigerian authorities have yet to respond.
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