The Syrian foreign ministry said in a statement on Thursday that Damascus had "expressed regret" for the violent protests when demonstrators set fire to the Norwegian and Danish embassies after newspapers in those countries published cartoons depicting Prophet Mohammad.
Svein Sevje, the Norwegian ambassador, said: "The responsibilities of Syria under the Vienna conventions is to secure the safety of foreign representation and their staff. The Syrians have acknowledged that.
"These bridges were not burnt by us. I think there is a basis to return to normal relations, whatever this means."
Sevje said he believed that Syria would pay for rebuilding the Norwegian embassy. Oslo has demanded compensation.
The ambassador said Norway was also encouraged by statements by Syrian religious leaders who said the anger over the cartoons should not be directed against foreign representation and that it hurt East-West dialogue.
Syria has stepped up security at Western embassies after coming under criticism from the West for failing to prevent the attacks. The demonstrators also damaged the Swedish embassy and tried to storm the French mission. No one was hurt.
"I don't think this was an attack on Norwegians per se. It was rage of some form or another on national symbols"
Sevje said: "We sent out a press release before the attack and asked to cool down the reactions. We also asked for more security for the embassy and when they sent an increased contingent of police it was clearly too late."
Norway advised its nationals to leave Syria after the attack on Saturday, but only a few left.
"We are taking our precautions but I feel fairly safe in Syria," Sevje said. "I don't think this was an attack on Norwegians per se. It was rage of some form or another on national symbols."