Speaking in Morocco, where he has been working with representatives of Libya's rival parliaments to nail down the agreement, Bernardino Leon blamed the delay on fighting around Tripoli over the past two days.
"For the moment, no one is leaving. We have had a difficult moment... and after these attacks there was a possibility either to cancel the dialogue or to lose some of the delegations," Leon told reporters.
Libya has two governments and parliaments, and on Friday the internationally recognised cabinet said loyalist forces had launched an offensive to "liberate" Tripoli.
The capital was seized in August by Fajr Libya, a militia alliance which includes Islamists that has installed its own government and legislature in Tripoli.
The Tripoli parliament's delegation threatened to walk out of the talks in the Moroccan resort of Skhirat when the fighting erupted.
But Leon said the delegates "agreed that at the end of the day, even with this military escalation, it is more important what we are trying to do here. It is more important to stay here."
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"Libya is not divided into two camps. Libya is fragmented," said Leon, adding that the delegates in Morocco have "strong support back home".
There would be further consultations Sunday and Monday aimed at preparing the documents on the unity government as well as security arrangements, he said.
"The documents... might be ready soon, maybe tomorrow (Monday) or after tomorrow and then we expect to start the next stage of the talks," Leon said.
"We will try to add to the two documents some principles that can be the basis for a final agreement."
Leon had hoped to nail a draft deal by Sunday, which would have capped three consecutive days of discussions.
But he said he spent the day consulting the delegates and insisted again "that since there is no military solution for Libya... they should stay and they should work" at clinching a political deal.
"I can confirm that everybody is on board, everybody is here and hopefully these consultations by tomorrow will produce positive results and all delegations will resume their work," he added.