The UN Security Council has urged Syria to implement "urgently and visibly" a peace plan requiring a 10 April deadline for ending a military offensive against the opposition.
Envoy Kofi Annan's plan calls for Damascus to pull back troops and heavy weaponry by that date, and for a full ceasefire by 48 hours later.
UN Secretary General Ban Ki-moon said the conflict was getting worse.
Mr Annan urged both sides to seize the moment and end the violence.
"Let us stop the killing and start a serious political dialogue," he told the UN General Assembly.
He said he expected a full ceasefire to take effect by 06:00 (03:00 GMT) on 12 April.
Syria has agreed to the plan, but its UN ambassador said that the main threat to the ceasefire came from the armed opposition backed by Qatar, Saudi Arabia and Turkey.
Bashar Jaafari demanded that Mr Annan obtain written guarantees from those countries that they were on board with the peace plan.
He also said that while troops and heavy weapons would be withdrawn from cities under the plan, police would remain "for the protection of the civilians".
Mr Annan is expected to travel to Iran on 11 April, the day after the partial ceasefire is due, to try to win further regional support for his peace plan.
The UN statement requested that Mr Annan provide proposals for a mechanism to supervise the ceasefire and update the Security Council on the cessation of violence and implementation of the peace plan.
The Security Council said it would consider further steps depending on the outcome of these reports.
Speaking later to the General Assembly by video link from Geneva, Mr Annan said he was urging the government and opposition to "issue clear instructions so that the message reaches across the country, down to the fighter and soldier at the local level".
He said that if the ceasefire was successful a small mobile UN monitoring mission of some 200-250 observers could be brought into Syria.
Syria had already reported some troop withdrawals from three cities, Mr Annan said, but the violence was still continuing.
"Alarming levels of casualties and other abuses continue to be reported daily. Military operations in civilian population centres have not stopped."
Activists reported on Thursday that government forces had been shelling several towns, including Homs, Deraa and the Douma suburb of Damascus.
There has also been a huge rise in the number of refugees crossing from Syria into Turkey, with 2,350 over a 24-hour period from Wednesday to Thursday, more than double the highest previous total.
The BBC's Jim Muir in Beirut says the activists are giving the clear impression that the Syrian regime is having a final crack at rebels before the ceasefire deadline.
Earlier Mr Ban urged members of the General Assembly to deepen their support for Mr Annan's efforts because of the deteriorating situation on the ground.
"Despite the Syrian government's acceptance of the joint special envoy's plan of initial proposals to resolve the crisis, the violence and assaults in civilian areas have not stopped," he said.
"The situation on the ground continues to deteriorate."
Meanwhile the International Committee of the Red Cross (ICRC) said that Syrian officials had agreed to it having an "expanded presence" in the country.
Speaking of the expanded Red Cross presence, ICRC President Jakob Kellenberger, who is at talks in Damascus, said: "This means that we will have to rapidly build up our human resources and logistical capacity in Syria.
"This agreement is a sign of trust in the ICRC's independent and neutral humanitarian action. It should enable the ICRC and the Syrian Arab Red Crescent to meet increased humanitarian needs."
The two sides also agreed procedures for humanitarian ceasefires and visits to places of detention, the ICRC statement said.
The UN says the conflict has cost more than 9,000 lives since it began a year ago. The Syrian government blames violence on "terrorist gangs" and says some 3,000 members of the security forces have been killed.
Foreign media face severe restrictions on reporting in Syria, and it is hard to verify the claims of either side.