Mugabe's Zanu-PF party and the opposition Movement for Democratic Change (MDC) are deadlocked over a power-sharing deal agreed in September as the economic and humanitarian situation deteriorates.
Morgan Tsvangirai, the prime minister-elect under the terms of the agreement, threatened to pull out of the deal on Friday saying dozens of members of his party had been abducted.
"The MDC can no longer sit at the same negotiating table with a party that is abducting our members, and other innocent civilians, and refusing to produce any of them before a court of law," he said at a news conference in Gaborone, Botswana's capital.
"If these abductions do not cease immediately and if all abductees are not released or charged in a court of law by January 1, 2009, I will be asking the MDC's national council to pass a resolution to suspend all negotiations and contact with Zanu-PF."
Mugabe said on Friday he had sent letters to Tsvangirai inviting him to be sworn in as prime minister.
"I have sent letters so that they can come and I can swear (in) and appoint them," he told supporters.
"We have not reached a stage where we can say with a degree of certainty that they (the opposition MDC) want to be part of this."
George Shire, a London-based Zimbabwe analyst, told Al Jazeera: "There is a political settlement deal on the table that offers Zimbabwe a future and hope.
"It's up to Zimbabweans to decide wether they think Robert Mugabe should lead them or not. He does have support within the country, he does have support within the region."
Mugabe and Tsvangirai insist they should take the interior ministry, which has stalled the power-sharing deal signed on September 15.
To try to resolve the stalemate, Frazer visited South Africa for talks with regional leaders.
"We think that the person who has ruined the country ... that he needs to step down," she said in an interview.
"There is a complete collapse right now ... we're watching Zimbabwe become a failed state. We need to act now, proactively, in Zimbabwe."
Botswana's foreign minister and Kenya's prime minister have both called for an end to Mugabe's 28-year rule.
But most of Zimbabwe's neighbours, including South Africa, the regional powerhouse, have rejected the possibility of military intervention and have repeatedly voiced their opposition to the idea.
Kgalema Motlanthe, South Africa's president, has said that he believed the proposed unity government was still the best way to resolve the situation and it should be formed quickly.
Al Jazeera's Haru Mutasa, reporting from Bindura where Mugabe's Zanu-PF were meeting for a policy conference, said "things are basically unbearable" for the majority of people in Zimbabwe.
"While the international community battles for a political solution in the country, millions of Zimbabweans are going hungry"
Oxfam humanitarian director
"If you don't have the US dollar you can't buy basic products in the supermarkets ... the Zimbabwe currency is pretty much worthless," she said.
Inflation in Zimbabwe has spiralled out of control and the prices of goods are doubling every 24 hours. Unemployment has risen above 80 per cent.
More than 1,000 people have died in a cholera epidemic exacerbated by a failing health care system and poor sanitation.
Suspected cases of the disease have shot up to more than 20,000 in the impoverished nation since the epidemic began in August, according to the UN Office for the Co-ordination of Humanitarian Affairs (OCHA).
Harare, the capital, is hardest hit with 224 people killed by the disease and more than 9,000 believed to be suffering it.
Nine out of Zimbabwe's 10 provinces have reported cases of cholera and the World Health Organisation (WHO) has said the total number of cases could reach 60,000 unless the epidemic is stopped.
The British charity Oxfam has asked international donors for $6m to fight the epidemic.
Oxfam said it was preparing to "substantially" scale-up its work in Zimbabwe, where it is providing food, water purification tables and soap to one million people.
"The rapid deterioration of the situation in Zimbabwe makes this an extremely grave humanitarian crisis which could deteriorate even further in 2009," Jane Cocking, Oxfam humanitarian director, said.
"While the international community battles for a political solution in the country, millions of Zimbabweans are going hungry."
Mugabe has blamed the West for the cholera outbreak accusing Britain and the US of using "biological weapons".
He has frequently attacked the West, including Britain, the former colonial ruler, accusing it of seeking to overthrow him and causing the the country's woes through sanctions.