The veteran leader, shunned by the West for his alleged attempts to suppress political opponents, received a warm welcome from Megawati.
She is considering sending a team to Zimbabwe to improve relations, especially in the trade sector, according to her foreign minister Hassan Wirayuda.
Megawati also invited Mugabe to pay an official visit to her country and to attend the 50th anniversary commemoration of the Asia-Africa Summit at Bandung in West Java in April 2005.
The Zimbabwean leader decided to open an embassy in Jakarta at the end of this year, Wirayuda said.
Indonesia already has an embassy in Harare while Zimbabwe's interests here are represented by its embassy in Kuala Lumpur.
Zimbabweans are currently suffering unprecedented economic hardships, with inflation running at 620% and unemployment estimated at 70%.
Wirayuda said Mugabe's visit was a private one and part of a swing through several Southeast Asian states including Malaysia and Singapore.
He said the two leaders discussed the need to enhance relations as well as issues in Zimbabwe such as the land acquisition campaign and the country's pullout from the Commonwealth.
The Commonwealth of former British colonies has suspended Zimbabwe from its ruling councils, prompting Mugabe to withdraw from the grouping last month in protest.
Mugabe is the subject of a travel ban imposed by the European Union and the US in March 2002 after he was re-elected in polls marred by alleged vote-rigging and violence.
The talks were also attended by Megawati's husband Taufik Kiemas and Environment Minister Nabiel Makarim.
On Tuesday Mugabe held talks with Prime Minister Abdullah Ahmad Badawi during a holiday visit to Malaysia, the New Straits Times said.
The two leaders are said to have reiterated their commitment to enhancing ties, particularly in trade and investment. – Sapa-AFP.
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