Secretary-General Annan's demand was released in a written statement on Thursday after he met with his special envoy, Terje Roed-Larsen, who recently visited the region as part of efforts to get Syria to adhere to UN Security Council resolution 1559 demanding Syria's withdrawal from Lebanon.
Annan made explicit in the statement that the withdrawal would include "the intelligence apparatus and military assets".
His call echoed one from US President George Bush, who also has called on Syria to withdraw all troops before the elections.
"The secretary-general further stressed the great importance that these elections be free and fair and take place as schedule," Annan said in the statement, read by his spokesman Fred Eckhard.
So far, Syria has pulled back army and intelligence agents to eastern Lebanon, with about 4000 troops having crossed into Syria.
About 10,000 troops remain along the Lebanese side of the border, and a date for a full withdrawal is to be set at a meeting of Syrian and Lebanese officers on 7 April.
Speaking to reporters on Thursday, Roed-Larsen pointedly would not say whether Syria had agreed to the timetable set out by Annan.
About 4000 Syrian troops have
move out of Lebanon thus far
That was somewhat surprising because on Saturday, after meeting Syrian President Bashar al-Asad, Roed-Larsen had indicated that he had extracted further details of a pullout timetable from Assad himself.
At the time, Roed-Larsen said he would take those details back to UN headquarters.
Roed-Larsen also said Annan had not laid out a way of enforcing the withdrawal but that it had wide backing from both "inside and outside the Security Council".
"There isn't an 'or else' - we simply expect that it happens," Roed-Larsen said, adding that al-Asad had given him "a clear and unequivocal commitment that he would meet his obligations under Security Council resolution 1559".
Hizb Allah factor
Resolution 1559 also calls for the disarming of militias in Lebanon - a clear reference to Hizb Allah's military wing. Roed-Larsen said there had been no decision on how to go about doing that.
He said he would return to the region in the first week of April to finish work on a report Annan will deliver to the Security Council on 19 April.
UN envoy Roed-Larsen will return
to the Middle East in early April
Syria sent troops to its smaller neighbour in 1976 to help quell what was then a year-old civil war. The troops, at times numbering more than 35,000, remained after the war ended in 1990.
Lebanon's opposition had long rejected Syria's role in their country, but the outcry intensified after the 14 February assassination of former prime minister Rafiq al-Hariri, seen as a powerful force moving into the opposition camp.
Tens of thousands of Lebanese have protested in the streets, and the international community re-issued demands that Syria implement the UN resolution.