The alliance's leader, Saad Hariri, said the Lebanese people had had their say and had voted for change.
Unofficial results from Sunday's polls give the bloc a majority in parliament.
A pro-Syrian leader of the group that challenged Mr Hariri in the final round of voting in northern
It was
He was killed in a bomb blast his supporters said was the work of
Syrian troops were stationed in
Aoun challenge
"The almost final results show that the people has had its say," Mr Hariri told the AFP news agency on Monday.
It has said that it wants change and that's what we call for."
Mr Hariri's coalition needed to win 21 seats on Sunday to reach a total of 65, the majority needed to control the 128-seat parliament.
In the fourth and final round of voting, the anti-Syrian alliance faced former General Michel Aoun's group in the fight for the last 28 seats at stake in northern
Although Mr Aoun's forces fought against the Syrians in the civil war, his allies in the election include pro-Damascus politicians, such as former Interior Minister Suleiman Franjieh.
His alliance did well in the third round of voting held in the
It would have had to secure a quarter of the 28 seats being contested in northern
However, our correspondent says, Gen Aoun's block of 21 seats have established him as the most significant Christian political figure whose views will be hard to ignore.
Bitter campaign
Mr Franjieh said his party accepted the popular will.
He told a local television channel: "Even if we have lost, we are the real representatives of the Christian areas in north
Official results are due later on Monday.
Saad Hariri is thought to have fared well in Sunni Muslim areas, with Mr Aoun's grouping taking the Christian vote, correspondents say.
Mr Hariri's group, which includes the Druze leader Walid Jumblatt and right-wing Christians, has so far secured 44 of the 100 seats polled so far in other parts of
The interior ministry said 49% of eligible voters turned out to cast their vote on Sunday, Reuters reports.
In earlier rounds the Amal and Hezbollah parties that have a pro-Syrian agenda won 35 seats.
PHOTO CAPTION
Saad Al-Hariri