United Nations (CNN) -- The Syrian government has agreed to begin immediately to pull its forces out of population centers and will complete its withdrawal by April 10, diplomatic officials told reporters Monday.
The Syrian foreign minister made that promise to U.N. special envoy Kofi Annan, according to Susan Rice, the U.S. ambassador to the world body. And Syria's ambassador to the United Nations, Bashar Jaafari, said Syria is committed to the success of Annan's peace plan, which calls for the withdrawal of Syrian forces as well as those of the opposition.
By then, all forward deployment of government forces and use of heavy weapons should be halted as well, Rice said after Annan briefed the Security Council in a private session.
She said officials were awaiting details from the Syrian government on other aspects of Annan's six-point peace plan, including requests for humanitarian access, a daily two-hour pause in hostilities and access for the news media.
"The Syrian government is committed, but we are expecting Mr. Kofi Annan and some parties in the Security Council also to get the same kind of commitments from the other parties," Jaafari said. He said those "other parties" were groups "involved in initiating, sponsoring and arming the armed groups."
All Security Council members called for the Annan plan to be implemented immediately, Rice said.
She noted that some members expressed concern that the government of Syria might use the coming days to ramp up the violence amid doubts about whether Damascus would be true to its word. But there was a general willingness to consider Annan's plan for a monitoring mission "if indeed cessation of violence is achieved," she said.
Annan did not specify any conditions for the deal, which was to have begun Sunday, Rice said. But the U.S. ambassador expressed skepticism over the Syrians' promise.
"Let's be realistic," she said. "We've seen commitments to end the violence followed by massive intensification of the violence. The United States would say yet again, the proof is in the actions, not in the words."
A diplomatic team that will include some of Annan's staff members will return this week to Syria "to continue preparations for monitoring a supervisory mission" of the United Nations, Rice said.
The announcement comes the same day that Russia -- historically a Syrian ally, which with China has blocked more stringent efforts to address the violence in the U.N. Security Council -- pressured Damascus to withdraw its troops.
"But if the withdrawal of troops is not accompanied by similar actions of those who fight against the Syrian government, I believe that no results will be yielded soon," said Foreign Minister Sergey Lavrov, according to the state-run Itar-Tass News Agency.
The United Nations has estimated at least 9,000 people have been killed in Syria since the unrest began more than a year ago -- violence that the Syrian government has blamed on "armed terrorist groups," but that the opposition and many other nations have said is a result of a crackdown on dissenters in the Middle East nation. Protesters want an end to the government of President Bashar al-Assad.
After yet another bloody weekend, at least 65 more people died Monday in fresh violence, according to opposition activists.
Seven soldiers from the rebel Free Syrian Army, four children and a woman were among those killed, the opposition Local Coordination Committees of Syria said. More than half of the deaths were in Homs, which has been a hotbed for dissent and bloodshed in recent months.
About 40 Free Syrian Army soldiers captured the National Hospital in that city, only to find 78 corpses stacked in a hospital refrigerator, the LCC reported Monday.
"We do not know who the bodies belong to, but it appears most of them are opposition from Baba Amr," said an activist in Homs, who was debriefed by the rebel army. Baba Amr is a Homs neighborhood that bore the brunt of weeks of shelling by government forces.
The LCC also said regime troops launched a campaign arresting people in Daraa province -- the cradle of the Syrian uprising -- and burned the homes of opposition activists.
About 8,000 refugees arrived Sunday night in Tirmaala, in the Homs district, and more came Monday to seek shelter, according to the opposition group. The group said that some single-family homes there were packed with more than 100 people.
Helping those in need is the focus of Jakob Kellenberger, the president of the International Committee of the Red Cross, as he starts two days of talks in Syria on Monday. He'll meet Syrian Foreign Minister Walid al-Mu'alem, Interior Minister Maj. Gen. Mohamad al-Shaar and Health Minister Dr. Wael al-Halki.
"I am determined to see the ICRC and the Syrian Arab Red Crescent expand their presence, range and scope of activities to address the needs of vulnerable people," Kellenberger said in a news release about his third such visit since June.
Meanwhile at the Vatican, the Pontifical Council "Cor Unum" announced that Pope Benedict XVI has donated $100,000 to support Syrians. The money will be used for the charitable activities of churches in Syria to "support ... the suffering population," the council said.
On Monday, the U.S. State Department announced it will provide an initial $1.25 million to establish a Syria Accountability Clearinghouse to help train Syrians and partner organizations to collect evidence related to human rights abuses and violations for possible use in any prosecutions that may result from the carnage.
This comes a day after U.S. Secretary of State Hillary Clinton pledged an additional $12 million in humanitarian aid -- nearly doubling the amount of American money pledged for humanitarian aid like field hospitals and medical training.
On Monday, State Department spokeswoman Victoria Nuland said that the United States has been providing "communications and medical support," and that officials are "looking at how we can expand that."
"Other countries made clear that they will be providing a different kind of support. They will be providing support directly to the Free Syrian Army," she said, in reference to the recently created armed force that is made up largely of defectors from Syria's military and is now the chief fighting force challenging al-Assad's regime.
Syria's ambassador to the United Nations blasted this and other promises of aid.
"All the parties who are sponsoring publicly the armed groups in Syria should bear the responsibility of their acts," Jaafari said. "This is a violation and a declaration of war against the sovereignty of Syria."
But Syrian National Council member Adib Shishakly said the international community needs to donate more, in order to meet the needs of the million-plus people affected by the violence in Syria.
"A million dollars daily, minimum, is needed," Shishakly said.
"If we don't bring protection for the people inside Syria, it's like we didn't do anything," he added, calling for international backing of the rebel Free Syrian Army, safe zones to protect people and relief and medical support.
CNN's Ivan Watson, Jill Dougherty and Kamal Ghattas contributed to this report.