Haile Menkerios's visit is the first by a UN envoy since 2005
A senior UN official has arrived in Zimbabwe for a five-day visit ahead of the presidential run-off vote, which continues to be marred by violence.
Haile Menkerios is expected to meet politicians to discuss the situation in the run-up to the election on 27 June.
Violence is reported to have spread to urban areas near Harare, with opposition activists complaining of being attacked near the capital.
The UK has meanwhile called Zimbabwe's government a "criminal regime".
Prime Minister Gordon Brown, meeting US President George Bush in London, said: "[President Robert] Mugabe must not be allowed to steal the election."
He also called for the UN to send a human rights envoy to Zimbabwe and for the country to accept international election monitors.
Meanwhile, the secretary-general of the opposition Movement for Democratic Change (MDC), Tendai Biti, did not make a scheduled appearance in court on treason charges.
His lawyer, Lewis Uriri, said Mr Biti had yet to be asked by police to make the formal written "warned and cautioned" statement required before he can be arraigned.
Tendai Biti was arrested on his return to Zimbabwe from South Africa
Mr Biti was arrested when he returned from neighbouring South Africa on Thursday and briefly appeared in court on Saturday, after his lawyers obtained a court order for the police to produce him and justify his detention.
At the time of his arrest, national police spokesman Wayne Bvudzijena said Mr Biti would be charged with treason "for publishing a document that was explaining a transitional strategy around March 26". The charge carries a possible death sentence.
Mr Uriri said the police were also planning to add a further charge of making statements intended to bring about disaffection in the security forces.
MDC leader Morgan Tsvangirai has been repeatedly detained during his presidential election campaign, but has so far faced no charges.
The visit of Mr Menkerios - the first by a UN envoy since 2005 - comes after sustained pressure from foreign countries and opposition politicians on President Mugabe to allow in international observers.
Last week the US ambassador to the UN, Zalmay Khalilzad, released a strongly-worded statement on Mr Menkerios's visit.
"If [Mr Mugabe] does not co-operate with Mr Menkerios and the current trends continue, we will have to deal with it. And we'll deal with it as quickly as we can."
The police have imposed a 12-hour curfew in parts of Masvingo province - one of those worst affected by recent violence.
A local police chief said most political violence was carried out at night and so ordered villagers to remain indoors after 1800 in Bikita and Zaka districts.
Political violence related to the presidential polls has swept the country in recent weeks, with thousands of people being displaced and dozens killed.
But it had been largely restricted to rural areas, especially those which had switched allegiance from Mr Mugabe's Zanu-PF to the MDC. Harare, traditionally an opposition stronghold, had remained relatively quiet.
However, at the weekend a local journalist reported a growing campaign of violence carried out by supporters of Zanu-PF in townships close to the capital.
Earlier, the president threatened to arrest opposition leaders for allegedly inciting political violence ahead of next week's run-off vote, in which he is due to face Mr Tsvangirai.
"There is now a pattern readable across the country and that has now to stop," he told a campaign rally in Kadoma, south of Harare.
"We are warning them that we will not hesitate to arrest them, and we will do that in broad daylight. They think they are protected by the British and the Americans. The law of the country has to be observed," he added.
MDC spokesman Nelson Chamisa dismissed the allegations.
"He is the one who has gone about threatening to go back to war if he loses. So while he is accusing us of violence, he is responsible," he told the AFP news agency.
Mr Tsvangirai won the presidential election's first round in March, but failed to win enough votes to avoid a second round, according to the official results.