"I have left Mutsamudu [Anjouan's main town] because that's where all the trouble is happening," Salim Sittina, who fled to join her family on Grande Comore, the largest of the country's three islands, said.
Said Ali Athoumane, a local trade unionist, said he was afraid of political reprisals.
"I have used up all my savings to save my skin," he said, adding that he had been in hiding for three days before fleeing to the neighbouring island of Moheli.
The federal government decided to delay the elections due to security concerns after Bacar loyalists killed two federal soldiers last month and police shot three people.
The African Union has "firmly condemned" the polls and declared Bacar's return to office "null and void". A delegation from the group, led by Nkosazana Dlamini-Zuma, the South African foreign minister, was due to arrive in Comoros later on Saturday.
Each of Comoros' three islands, whose total population is 670,000, retain autonomy through local presidencies under the terms of a 2001 peace deal and share a rotating national presidency.
Last year's national presidential elections were Comoros' first peaceful transition of power since independence in 1975. It has suffered 19 coups or attempted coups since then.