President Seretse Khama Ian Khama's decision not to attend the summit in South Africa underlines growing pressure from regional leaders on Mugabe and the opposition to agree on sharing power to end post-election turmoil.
Power-sharing negotiations began last month after Mugabe's unopposed re-election in June, which was condemned around the world and boycotted by opposition leader Morgan Tsvangirai because of attacks on his supporters.
Three days of marathon meetings in Harare this week failed to reach an overall deal.
Botswana's foreign ministry said in a statement that Zimbabwe's current government should not be represented at a political level of the 14-member Southern African Development Community (SADC).
"Botswana does not accept the result of the June 27 run-off election in Zimbabwe as it violated the core principles of SADC, the African Union and the United Nations," the statement said.
Zimbabwe's ruling ZANU-PF and the opposition will resume power-sharing talks at the summit, a ZANU-PF official was quoted as saying on Friday.
"We are travelling to South Africa with President Mugabe today as the negotiations continue," the state-owned Herald newspaper quoted the ruling ZANU-PF's chief negotiator, Patrick Chinamasa, as saying.
"The talks never collapsed and all parties are committed to the dialogue. I would also want to confirm ZANU-PF's commitment to see the talks end successfully sooner rather than later."
Nic Borain, political consultant to HSBC Securities, said behind-the-scenes manoeuvring by supporters of both sides may be the biggest obstacle to an agreement, hindering efforts to end an economic catastrophe.
"You have Tsvangirai's backers who are playing hardball and insisting on the virtual disappearance of Robert Mugabe, and you've got Robert Mugabe's backers insisting he remains, maintains some kind of executive powers," he said.
Chinamasa said there was pressure for the country to convene parliament and form a government.
"We cannot continue wandering around without direction, hence the need to swear in parliamentarians and open the House so that the elected members can continue to fulfil their constitutional mandate," he said.
Tensions mounted on Thursday, when Zimbabwean authorities briefly confiscated Tsvangirai's passport, threatening to prevent him attending the summit, an official of his Movement for Democratic Change said. The MDC leader arrived in South Africa on Friday.
On Friday, the MDC condemned what it called "corrosive" attempts by ministers and intelligence agents to recruit some of its members to join Mugabe's government.
"These are the actions of a desperate and cornered regime," it said in a statement.
Tsvangirai's absence from a new government would do nothing to dispel investors' concerns about a country facing economic ruin, with the world's highest inflation of 2.2 million percent, chronic food and fuel shortages, and high unemployment.