At least 87 people were killed in violence on Tuesday alone, he was quoted as saying. Syrian security forces sometimes cut power to towns targeted by operations.
The basic message was that Syria has "not heeded" the council's calls to end the violence, said one diplomat as consultations continued.
Western nations will use the Security Council meeting to test reaction to possible stronger UN steps against Assad, diplomats from various countries said.
The United States called for greater international pressure on Assad ahead of the meeting of the 15-nation body. But the US ambassador, Susan Rice, expressed doubt that the Security Council was ready to agree on a resolution threatening sanctions against Assad.
"We are going to continue and intensify our pressure both through our national actions, in additional sanctions, as well as coordinated efforts with other partners here in New York and around the world," Rice told reporters.
"In the view of the United States, he has lost his legitimacy to rule and Syria would be a better place without him," the ambassador added.
"We are looking to the future and looking to lend support to the people of Syria who have the same aspirations for freedom and democracy that we have seen in so many other parts of the world."
The Security Council passed a statement last week condemning the violence and calling for Fernandez-Taranco's report. Russia and China have led opposition to a formal UN resolution, however, with the support of Brazil, India and South Africa.
With the same countries still angry over NATO air strikes in Libya, Western nations say it will be difficult to win the required majority for a sanctions resolution against Syria.
"I am loath to predict how exactly the council will respond in the future," Rice said.
Asked whether the council could refer Assad to the International Criminal Court, as it has with Libya's Moamer Kadhafi, Rice said she doubted it would get the required support now.
But she added: "To the extent that we have evidence of crimes, we would share that quite readily with any in a position to investigate."
"I think members have been moved by what they have seen of late and by the intensifying and horrific violence that we have seen against civilians. But we have also been frustrated quite candidly that it has taken as long as it has for the council to speak with one voice," she said.
"It is past time for all council members to put the interests of the Syrian people rather than particular bilateral issues or interests at the forefront of their actions."
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