The question is key, because the council a little more than a week ago unanimously approved a new resolution ordering Syria to cooperate fully with a UN investigation into the assassination of former Lebanese prime minister Rafiq al-Hariri or face possible unspecified "further action".
After that 31 October vote, US Secretary of State Condoleezza Rice said the measure "made it clear that failure to comply with these demands will lead to serious consequences from the international community".
Tuesday's verbal clash began when Annan, in Cairo for a meeting with Egyptian Foreign Minister Ahmed Aboul Gheit, told reporters Damascus "has had a good record" in implementing Security Council resolutions.
Bolton, asked in New York about Annan's statement, said Syria's performance in carrying out council resolutions had ranged from "very lacking" to "substantially lacking".
Asked whether Annan's words were helpful to the council, Bolton responded: "I think I will not comment on his comment."
The 15-nation council has passed a number of resolutions in the past 14 months dealing with Syria's domination of neighbouring Lebanon and with al-Hariri's 14 February assassination.
Annan: Syria had a good record in
A resolution adopted on 2 September 2004, demanded the withdrawal of foreign forces from Lebanon, a disbanding of militias in Lebanon and an end to Syrian meddling in Lebanon.
A second, approved on 7 April 2005, authorised an international investigation into al-Hariri's murder.
Syria to investigate
After the September 2004 resolution, Syria withdrew its forces from Lebanon and Lebanon held parliamentary elections free of Syrian interference.
Acting on the April 2005 text, Detlev Mehlis, who leads the UN inquiry into al-Hariri's death, accused the Syrian authorities last month of obstructing his work and said the killing could not have been plotted without the knowledge of Syrian security officials and their Lebanese allies.
Annan, in Cairo, said Syrian President Bashar al-Assad had assured him of Syria's intention to cooperate with Mehlis and praised Syrian implementation of the September 2004 measure.