Some 5,000 Syrians die monthly in the civil war and more than 6,000 people on average flee the country every day, U.N. refugee and humanitarian officials said.
Of the nearly 1.8 million refugees identified by the U.N. Refugee Agency, two-thirds have fled this year, U.N. High Commissioner for Refugees Antonio Guterres  told the Security Council by satellite link from Geneva, Switzerland.
"We have not seen a refugee outflow escalate at such a frightening rate since the Rwandan genocide almost 20 years ago," Guterres said.
"I reiterate my call to all states, in the region and further afield, to keep borders open and receive all Syrians who seek protection," the former Portuguese prime minister said, urging governments to do all they could to balance measures to prevent dangerous "infiltrations" with the need to help refugees seeking safety.
He specifically cited families, elderly people and women with children.
Without help, all refugees might otherwise get caught in the fighting, he said.
U.N. Assistant Secretary-General for Human Rights Ivan Simonovic told the 15-member council nearly 93,000 people in Syria had been killed in the first 25 months of the 28-month-old conflict, which started in March 2011.
The war dead through April included more than 6,500 children, he said.
"The extremely high rate of killings nowadays -- approximately 5,000 a month -- demonstrates the drastic deterioration of the conflict," Simonovic said.
Syrian Ambassador to the United Nations Bashar Jaafari disputed the death toll, calling it "unprofessionally sourced." Jaafari also criticized the use of a U.S. company to collect the information for the agency.
Simonovic insisted "rigorous" methods were used. He said each victim's identity was verified by name and date and cross-checked with at least three sources.
Undersecretary-General for Humanitarian Affairs and Emergency Relief Coordinator Valerie Amos told the council at least 6.8 million Syrians needed urgent humanitarian aid.
She accused both the regime of President Bashar Assad and opposition forces of "systematically and, in many cases, deliberately" failing to protect civilians.
At least 77 people were killed in Syria Tuesday, the opposition Local Coordination Committees reported. The dead included eight women, five children and four detainees tortured to death, the network of local groups said.