An estimated 5,000 Syrians are dying every month in the country's civil war and refugees are fleeing at a rate not seen since the 1994 Rwanda genocide, U.N. officials said Tuesday.

"In Syria today, serious human rights violations, war crimes and crimes against humanity are the rule," said Ivan Simonovic, the assistant secretary-general for human rights, told the U.N. Security Council on Tuesday.

He added that "the extremely high rate of killings ... demonstrates the drastic deterioration of this conflict."

U.N. refugee chief Antonio Guterres said two-thirds of the nearly 1.8 million Syrian refugees known to the agency have fled since the beginning of 2013, an average of over 6,000 daily.

"We have not seen a refugee outflow escalate at such a frightening rate since the Rwandan genocide almost 20 years ago," he said.

U.N. humanitarian chief Valerie Amos said at least 6.8 million Syrians require urgent humanitarian assistance and accused the government and opposition of "systematically and in many cases deliberately" failing their obligation to protect civilians.

"This is a regional crisis, not a crisis in Syria with regional consequences, requiring sustained and comprehensive engagement from the international community," Amos said by videoconference from Geneva.

"The security, economic, political, social, development, and humanitarian consequences of this crisis are extremely grave and its human impact immeasurable in terms of the long-term trauma and emotional impact on this and future generations of Syrians," she said. "We are not only watching the destruction of a country but also of its people."

Simonovic said that since U.N. human rights chief Navi Pillay reported last month that at least 92,901 people had been killed between March 2011 when the conflict began and the end of April 2013, government forces and militias have moved to uproot the opposition in many areas including Qusair and Talkalkh, Aleppo, Damascus and its suburbs.

"Government forces carry on with indiscriminate and disproportionate shelling and aerial bombardments, using among other weapons tactical ballistic missiles, cluster and thermobaric bombs, all causing extensive damage and casualties if used in densely populated areas," he said.

"As a result, hundreds of civilians, including women and children were killed, thousands injured, and tens of thousands displaced," Simonovic said. "Many displaced in the parts of Homs and rural Damascus remain under siege and face miserable humanitarian conditions."

He said armed opposition groups have also committed acts of torture, abduction and kidnapping, sometimes along sectarian lines.

"Killings, violence and threats of reprisals against civilian populations perceived to be supportive of the government by armed opposition groups are escalating alarmingly," he said.

Guterres, the refugee chief, said "the danger that the Syrian conflict could ignite the whole region is not an empty warning."

Calling the impact of the refugee crisis on neighboring countries "crushing," he urged international action to support the stability of Syria's neighbors and reduce "the enormous risks of spillover" to the wider Middle East.

Guterres appealed to all countries to keep their borders open and receive all Syrians who seek protection.

Lebanon and Jordan are bearing the heaviest burden of the refugee exodus, he said, but the Kurdish region of Iraq and Turkey which has spent hundreds of millions of dollars of its own resources to assist over 400,000 refugees have also been affected.

"What I am asking for today is essential to mitigate the risk of an explosion that could engulf the entire Middle East, but only a political solution to Syria and an end to the fighting can fully stop this risk," Guterres said.

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Syria's U.N. Ambassador Bashar Ja'afari said the U.N. death toll and refugee figures came from "unprofessional sources" and insisted the Syrian government was doing "everything possible to shoulder its responsibilities to its people and meet basic needs despite economic, political and media pressure."

He said the government is fighting "terrorism" — its description of opposition fighters. He asked why the world was only concerned about 2,500 people trapped in Homs and not hundreds of thousands trapped elsewhere in Syria.