Ali Mohamed Shein’s term in office was due to expire on Monday.
He was seeking re-election as the ruling CCM’s candidate; his rival Seif Sharif Hamad has declared himself the winner of the 25 October vote.
Tanzania’s outgoing leader says he is mediating to find a peaceful outcome.
Over the weekend, two small bombs exploded on the main island of Zanzibar – no casualties were reported.
Previous elections on Zanzibar – a popular tourist destination – have been marred by riots and violence.
Correspondents say there is a heavy troop presence on the streets.
Mr Hamad, the opposition Ukawa candidate, asked his supporters to “remain calm and observe peace” on Monday as “diplomatic efforts have been going on well,” the AFP news agency reports.
A statement from Zanzibar’s government said Mr Shein would remain in office until fresh elections were held.
The office of Tanzanian President Jakaya Kikwete, who is stepping down after two terms in office, is brokering talks between the Zanzibari opposition and the country’s army chief.
International observers say the nationwide elections were largely “free and fair”, but all groups raised concerns over the subsequent annulment of Zanzibar’s local elections.
Zanzibar’s election chief Jecha Salim Jecha said the polls for the archipelago’s parliament and president had been marred by gross irregularities, including rigging and physical fights between rival election commissioners.
Governing CCM party candidate John Magufuli won the national presidential election with 58% of the vote.
Source: 3news.com
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