Speaking to reporters on Thursday Annan's spokesman Stephane Dujarric said the Secretary General had "absolutely no disagreement" with Arbour's statment, and had "full confidence" in her as "a highly respected jurist".
On Wednesday, Arbour, the Canadian-born UN High Commissioner for Human Rights, said two practices reportedly used by the United States in its war on terror were having "a corrosive effect on the global ban on torture".
She referred to "the use of secret detention facilities and the seeking of diplomatic assurances to avoid what would otherwise be the total prohibition on rendering, surrendering, deporting, turning back people to countries where they may face the risk of torture".
And Arbour reminded Washington that the 1984 convention against torture, which has been ratified by 140 states, "prohibits recourse to torture, cruel degrading and other inhumane treatment at the instigation of agents of the state for the purpose of obtaining intelligence or other types of information".
Her comments were seized upon by US ambassador to the UN John Bolton.
He said it was "inappropriate and illegitimate for an international civil servant to second guess the conduct of what we are engaged in the war on terror with nothing more as evidence than what she reads in the newspapers".
Commenting on the row, Annan's spokesman said the secretary general was confident Arbour would carry out her work "without being intimidated by what happened yesterday" and planned to discuss the incident with Bolton "at an early date".
He said the UN chief felt that "international civil servants should be allowed to speak freely" in their area of competence.
In Kiev, US Secretary of State Condoleezza Rice said on Wednesday that US personnel were banned from using torture anywhere in the world, in an apparent attempt to quell a raging controversy in Europe over secret CIA prisons.
An aide to Rice said her remarks marked "a clarification of policy, not a shift of policy".
Claims have been mounting that the United States has been illegally using European airports and airspace to transport terrorism suspects as part of what the US Central Intelligence
Agency calls "extraordinary renditions".
Rice has described rendition as "a vital tool" in countering "transnational terrorism", and said that the governments of countries through which "rendered" detainees were transported were consulted.