Opposition leader Tsvangirai, meanwhile, threatened to ask for a suspension of power-sharing talks if the government did not stop what he called the persecution of political opponents.
The deadlock between the two has held up any chance of ending the spiralling crisis in the southern African country, where a spreading cholera epidemic has killed more than 1,100 people and food and fuel are in short supply.
Mugabe told supporters he had sent letters to Tsvangirai inviting him to be sworn in as prime minister but expressed doubt that a breakthrough could be reached.
"I have sent letters so that they can come and I can swear (in) and appoint them. We have not reached a stage where we can say with a degree of certainty that they want to be part of this," Mugabe said.
But Tsvangirai’s opposition Movement for Democratic Change said that it had not received any letters.
Tsvangirai says the talks on the power-sharing agreement with Mugabe, reached in September, are endangered by what he calls a wave of abductions of MDC supporters and other anti-Mugabe activists. The opposition blames Mugabe’s ZANU-PF party.
"If these abductions do not cease immediately, and if all the 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," Tsvangirai said in a news conference in Gaborone.
Tsvangirai defeated Mugabe in a March presidential election but without an absolute majority. He pulled out of the run-off in June, saying scores of his supporters had been killed.
His threat came amid growing international concerns over the spread of a cholera epidemic in Zimbabwe and renewed calls from Western countries and some African leaders for Mugabe, 84, to step down or be ousted.
The United Nations reported that the death toll from the cholera epidemic had risen to 1,123 and that 20,896 people had been infected with the easily preventable and treatable disease as of Thursday.