The family of a New Zealander murdered in Hungary say they are living a nightmare and are focusing on bringing his body home.

Warwick White, 48, a competitor in the world triathlon championships, died in the capital, Budapest, early on Sunday after being stabbed in the chest.

A 32-year-old man known to the police was arrested less than 24 hours after the attack.

The slain Kiwi's son-in-law, Dylan Thomsen of Wellington, said Mr White's sister left for Hungary yesterday to collect her brother's body.

Budapest deputy police chief Valter Fulop told a press conference that Mr White had been arguing with a prostitute when the man intervened.

The New Zealander was stabbed several times in the chest, with one wound penetrating his heart.

Mr White died on the way to hospital, and a hotel key in his possession helped to identify him.

Mr Fulop said the arrested man had denied responsibility for the attack but police had enough evidence to prosecute him. He has previously been convicted of violent offences.

Mr Thomsen said the family had received no official word about the arrest.

"Obviously we've seen the reports but we don't know anything. There are criminal processes going through over there and so we are just waiting. It makes it tough ... It's just a nightmare to go through."

Suze Randal from Rongotai College in Wellington said staff members who remembered Mr White, who taught physical education there from 1988 to 1990, would be saddened.

"He had a passionate love of the outdoors. He was a very talented, confident and capable teacher."

Mr White was in Hungary competing at the world champs in the 45-49 age group.

He finished 38th in the men's sprint event, representing Ecuador, where he had been living.

He had spent around eight years in South America and in Europe and had planned to visit family in Christchurch and Wellington for Christmas.