The extension takes effect immediately.
The announcement came a day after Jammeh declared a three-month state of emergency as he seeks to stay in power despite losing elections in December. President-elect Adama Barrow has vowed to be sworn in tomorrow, with the backing of the international community.
As the political crisis deepened, special flights were being organised to evacuate British and other tourists from Gambia, where the threat of a regional military intervention loomed to force Jammeh to step down.
Thousands of people have been fleeing the tiny country, including a number of government ministers. Barrow is in neighboring Senegal for his safety.
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Travel group Thomas Cook said it planned to bring home nearly 1,000 vacationers, and four flights were being added today.
The evacuation was not mandatory, but offered those who want to leave the option.
Many tourists seemed unaware and continued to enjoy lying on the beach. While Jammeh's government has been accused by human rights groups of arbitrary detentions and torture of opponents during his 22-year rule, the government has promoted Gambia as "the smiling coast of Africa."
Another Dutch tour operator, Tui, was sending five aircraft to repatriate Dutch and Belgian tourists. Tui said it had 815 Dutch tourists and 228 Belgians in the country.
Tui spokeswoman Petra Kok said the company was making it clear to tourists that if they decide to stay, it is their own responsibility.
The Dutch government has a negative travel advisory in place for tourists wanting to visit the country.
The new state of emergency bans people from "any acts of disobedience" or violence, and it tells security forces to maintain order.
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