The Israeli warning shot across the UN-monitored ceasefire line between Syria and the occupied Golan Heights came after a mortar round fired from the Syrian side hit an Israeli position.
It came after Prime Minister Benjamin Netanyahu told his cabinet Israel was "ready for any development" and as his defence minister warned a "tougher response" would follow.
"Our people are subjected to a systematic genocide," Khatib said at the signing ceremony, urging the international community to "fulfill its pledges".
The recently-elected head of the SNC George Sabra who also signed the final draft of the agreement said that Syrian rebels need weapons "not just bread and water".
Qatari Prime Minister Sheikh Hamad bin Hassem Al-Thani said he will accompany Khatib on Monday to the Arab League's headquarters in Cairo.
"We will seek a full recognition of this new body," Sheikh Hamad said.
Reservations in SNC ranks about what many members saw as a move to sideline it had prompted repeated delays in the Doha talks and mounting frustration among other dissident groups and the opposition's Arab and Western supporters.
But after negotiations ran into the early hours of Sunday and resumed in the afternoon, the anti-Assad factions agreed to form a "National Coalition of Forces of the Syrian Revolution and Opposition."
"We signed a 12-point agreement to establish a coalition," said Seif, who championed the US-backed reform proposals on which the agreement was based.
In a copy of the document obtained by AFP, the parties "agree to work for the fall of the regime and of all its symbols and pillars," and rule out any dialogue with Assad's government.
They agreed to unify the fighting forces under a supreme military council and to set up a national judicial commission for rebel-held areas.
A provisional government would be formed after the coalition gains international recognition, and a transitional government after the regime has fallen.
Former Syrian premier Riad Hijab who defected in August hailed the agreement as "an advanced step towards toppling the regime."
The deal came after the SNC, previously seen as the main opposition group, heeded Arab and Western pressure to embrace groups that had been unwilling to join its ranks.
Khatib, the imam of the central Umayyad mosque in Damascus before he was arrested for supporting the uprising, is seen as an independent as he is not linked to the Muslim Brotherhood or any other Islamist party.
His deputies also hail from mixed backgrounds, with Seif reportedly backed by Washington and Atassi belonging to a Homs family active in the secular opposition. A third vice president post will remain vacant for a Kurd.
Britain hailed the agreement as an "impportant milestone in forming a broad and representative opposition that reflects the full diversity of the Syrian people."
-- Mounting diplomatic pressure --
France hailed the Doha signing and it was lending its "full support to this coalition, in order for it to become a credible alternative" to Assad's regime.
There had been mounting pressure for an overhaul amid US-led accusations that the SNC had lost touch with civilian activists and rebels inside Syria and become little more than a talking shop for exiles.
Concern had been further raised by fears of a spillover of the conflict as fighting raged on Syria's borders with Iraq and Turkey as well as on the armistice line with the Israeli-occupied Golan.
The Israeli army said a mortar round fired from the Syrian side had hit one of its positions on the Golan plateau, prompting the riposte from its troops.
"A mortar shell hit an IDF (Israel Defence Forces) post in the Golan Heights... as part of the internal conflict inside Syria," it said, adding that "in response, IDF soldiers fired warning shots towards Syrian areas."
Chief military spokesman Yoav Mordechai said it was Israel's first firing across the armistice line since the 1973 Middle East war.
And Defence Minister Ehud Barak warned later that Israel would strike back even harder in response to any more fire from Syria.
"Syria has been in the midst of a brutal civil war for over a year, and the IDF has been instructed to prevent the battles from spilling over... Additional shelling into Israel from Syria will elicit a tougher response, exacting a higher price from Syria," he warned.
Fighting also flared on the Turkish border as Syrian troops and rebels battled for the town of Ras al-Ain, where thousands of refugees have fled into Turkey in recent days, said the Syrian Observatory for Human Rights.
Ras al-Ain is one of just two Turkish border crossings the Syrian army still controls. Rebels fighting to bring down Assad have captured four others while a seventh is controlled by Kurdish militia.
Nationwide violence killed at least 86 people on Sunday, including 34 civilians, the Observatory said, among more than 37,000 who have lost their lives since the uprising erupted in March 2011.