The wrangling over the UN draft plan came as militants from the North African nation's Islamic State affiliate seized new territory, inching closer to a major city and oil terminals, virtually Libya's sole source of state revenues.
The threat of the Islamic State group, which already holds two cities and several towns in Libya, is one of the factors fueling the United Nations' push to resolve the country's chronic chaos. European countries fear the extremists will gain a larger bastion just across the Mediterranean.
Since early last year, Libya has been split. In the capital Tripoli and most of the west, militias backing Islamist political factions are in control, and the Islamists have set up their own parliament and government.
The east is mainly held by the anti-Islamist parliament elected last year, which is recognized internationally and backed by remnants of the Libyan army led by powerful general Khalifa Hifter.
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The two sides have been fighting for months, with neither able to gain an advantage over the other.
"There is a general sense of hope, I would say even optimism ... But still we have to cautious."
After the elected parliament announced its suspension, UN spokesman Stephane Dujarric said, "We all remain hopeful the parties will support the agreement."
Since the ouster and killing of longtime dictator Moammar Gadhafi in the 2011 civil war, Libya has been in chaos.
The crisis was exacerbated when a militia force known as Libya Dawn, made up mainly of fighters from the third-largest city Misrata, took over Tripoli last year, allowing the Islamist factions including the Muslim Brotherhood to set up their government while the anti-Islamist government fled east.