Syria crisis: 'Limited progress' on aid - Valerie Amos
She gave more details about the "terrible" state of Baba Amr district in Homs, where "every building" was hit by the weeks of army bombardment.
Earlier, opposition activists rejected calls for dialogue by envoy Kofi Annan.
Burhan Ghalioun, the leader of the main opposition, said the comments were "disappointing" when Syrians were being "massacred every day".
Mr Annan, who is due in Syria on Saturday, had said a solution lies in a "political settlement".
He also said further militarisation "would make things worse".
Mr Annan is scheduled to meet Syrian President Bashar al-Assad at the weekend.
Meanwhile, several senior Syrian military officers have defected and fled into Turkey.
The Turkish government has confirmed media reports that two generals, a colonel and one other officer were among 230 Syrians who crossed the border on Thursday.
'No building unaffected' Baroness Amos, who visited the city of Homs - including the bombed-out district of Baba Amr this week - said the government had indicated that an initial humanitarian assessment could be made within the next week, and that a UN team in Damascus was ready to get to work.
"I put to them a quite comprehensive agreement which I had hoped to get signed," she told the BBC.
"They have agreed to a limited preliminary assessment to try to find out where people are and what they need, but I would like something much more comprehensive.
"They have undertaken to look at that and get back to me and I don't know how long that will take."
The UN aid chief described a "terrible situation" in Baba Amr, which was vacated by rebels last weeks after a massive government bombardment lasting several weeks.
She said there was not a single building in the areas she had visited which had not felt the impact of the bombardment.
There were large holes in the streets and evidence of tanks rolling through, she added.
Baroness Amos has also toured camps on the Turkish-Syrian border where about 11,000 Syrians have taken refuge.
Tens of thousands of people were again reported to be on the streets across Syria on Friday, protesting against the Assad regime.
Activists from the UK-based Syrian Observatory for Human Rights said there were big demonstrations in Deraa, Latakia, Homs, Hama, Deir Ezzor and Aleppo.
The Local Co-ordination Committees, another rights group, said 46 people were killed across Syria on Friday, including 22 in Homs, 11 in Idlib, five in Deraa, four in Hama, two in Damascus and one each in Latakia and Aleppo.
'Tanks massing' Meanwhile, activists and the Observatory said troops backed by tanks were massing in Idlib, near the Turkish border, to target the Free Syrian Army (FSA), the country's main rebel military force.
Some activists fear Idlib could suffer the same fate as Baba Amr.
The UN says more than 7,500 people have died as a result of the violence in Syria over the past 12 months.
In other diplomatic moves on Friday, Russia said it could not back a new UN draft resolution on Syria as it was "unbalanced".
Deputy Foreign Minister Gennady Gatilov told Interfax: "Its main problem is the absence of a simultaneous call on all sides to take practical steps in the context of ceasing fire."
The draft resolution demands the Syrian government "immediately" ends violence while calling on opposition groups to "refrain from all violence".
Russia and China have jointly vetoed two previous UN Security Council drafts.