Activists says several towns, including Homs, Deraa and the Douma suburb of Damascus, have been shelled .
There are also reports of a steep rise in refugees crossing into Turkey.
A spokesman for Mr Annan said Syria had reported some troop withdrawals and the UN expects a full truce by 12 April.
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.
The UK-based Syrian Observatory for Human Rights group has reported fresh clashes in the southern village of Kfar Shams and Douma in Damascus, where it said columns of smoke could be seen rising from several buildings.
One activist in Douma, Mohammed Saeed, reported that soldiers were using detainees as human shields.
“Soldiers in the Ghanam Square near the vegetable market were walking behind detainees,” he told the Associated Press news agency. “They do that so that members of the Free Syrian Army do not open fire at the troops.”
The opposition also said security forces were trying to storm two villages in northern Aleppo province, close to the Turkish border.
Activists say dozens of people have been killed in recent clashes.
The human rights group Amnesty International said it had counted 232 deaths since Syria accepted Mr Annan’s six-point peace plan last week.
The BBC’s Jim Muir in Beirut says activists are giving the clear impression that the Syrian regime is having a final crack at rebels before the ceasefire deadline.
Speaking in Geneva on Thursday, Mr Annan’s spokesman, Ahmad Fawzi, told reporters their team was trying to verify Syria’s assertion that it has withdrawn some troops.
“They have specified three cities – Deraa, Idlib and Zabadani,” he said.
‘Clock starts ticking’
Mr Fawzi added that Mr Annan will travel to Iran on 11 April, the day after a partial ceasefire is due, to try to win further regional support for his peace plan.
He said both sides have agreed to a ceasefire on 10 April and then the “clock starts ticking” as they will then have 48 hours to end hostilities.
Mr Annan, the UN and Arab League special envoy, is due to address the UN General Assembly later.
But the French Foreign Minister Alain Juppe has warned he is not optimistic that Mr Annan’s peace plan will be successful.
“Can we be optimistic or not? I am not, because I think [Syrian President] Bashar al-Assad is tricking us,” Mr Juppe said. “He is pretending to accept Kofi Annan’s six-point plan while at the same time still using force”.
The advance UN team in Damascus is being led by Maj Gen Robert Mood, a Norwegian who has extensive peacekeeping experience.
He hopes to agree with the Syrian government how a mission of 250 unarmed observers will be structured and how it will operate after a full ceasefire is declared.
The UN has started asking member states to commit troops.
Meanwhile, a Turkish official said up to 900 more people had fled across the border from Syria.
“There has been an increased flow through Reyhanli and the number was 800 to 900 [on Wednesday],” the official told Reuters.
There are now almost 21,000 Syrian refugees in Turkey.