The more than two-year civil war between the Syrian regime of President Bashar al-Assad and various rebel factions has caused the worst refugee crisis in two decades, with an average 6,000 people per-day fleeing the country, the United Nations said Tuesday.

The world has "not seen a refugee outflow escalate at such a frightening rate since the Rwandan genocide almost 20 years ago," said UN refugee chief Antonio Guterres.

His remarks came at a rare public briefing in which UN aid chief Valerie Amos also warned that at least 6.8 million Syrians were now in need of urgent aid. "We are not only watching the destruction of a country but also of its people," she said.

Ivan Simonovic, the assistant secretary-general for human rights, announced that at least 92,901 people have been killed in Syria, including more than 6,500 children, between March 2011 and April 2013.

"The extremely high rate of killings nowadays — approximately 5,000 a month — demonstrates the drastic deterioration of the conflict," Simonovic told the council.

And as the UN pointed out, the Syrian conflict is not confined to Syria, as neighboring nations in the region have slowly begun to feel its destabilizing effect, with violent spillovers reported on their borders and in their countries.

More from GlobalPost: Syria's refugee crisis hits children especially hard (PlanetPic)

“This is a regional crisis not a crisis in Syria with regional consequences, requiring sustained and comprehensive engagement from the international community,” Amos said.

Amos also noted that $3.1 billion was still required to provide aid to Syrians, many of whom now live in Lebanon, Jordan, Turkey, Iraq and Egypt. According to the World Food Program's latest estimate, some 4 million Syrians are unable to meet their basic needs, as the civil war has destroyed families' ability to buy or grow food.

This GlobalPost On Location video illustrates the human angle of the refugee crisis:

The UN Security Council, which includes veto-power states China, France, Russia, the United Kingdom, and the United States, has been in a diplomatic deadlock on how to go about trying to solve the conflict that has in recent months turned increasingly sectarian.

Meanwhile, crimes against humanity, war crimes and other human rights violations have been reported on both sides.

Both Russia, an ally of Assad, and China have blocked UN action against the Syrian president, even when it was supported by the other members.