Waheed, who took office when the first democratically elected President Mohamed Nasheed resigned under duress in February 2012, had been under pressure from India and western powers to step down after his tenure ended on November 10.
He told the media he would pay a private visit to Singapore. Though he said he would come back to the Maldives, Waheed did not specify a return date, Haveeru portal reported.
CMAG expressed "deep disappointment" that the Maldives presidential election process had not concluded prior to the expiry of Waheed's term in office.
India too has expressed its disappointment with the postponement of run-off polls till November 16 and said a new President should be sworn in at the earliest.
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A run-off between Nasheed, who led the first round of the presidential polls on November 9, and his rival Abdulla Yameen is scheduled for tomorrow.
The first election on September 7 was annulled by the Supreme Court, citing the rigging of voters' lists, while the Elections Commission's attempt to hold polls on October 19 was thwarted by police after a Supreme Court ruling.
In a televised address to the nation last night, Waheed claimed his government had refused to bow down to foreign pressure and upheld the legal framework and orders of the constitutional institutions of the country.
Waheed said that after working under a legal framework that constrained the powers of the President for decades, it was only patience and compromises that paved the way for an election where three candidates were competing.