The US ambassador to the UN, John Bolton, had demanded Kofi Annan should repudiate Mark Malloch Brown's remarks.
Bolton described Tuesday's speech as a "very, very grave mistake" that could undermine efforts to reform the organisation.
"Even though the target of the speech was the United States, the victim, I fear, will be the United Nations," Bolton said at the UN on Wednesday after speaking to Annan.
Annan, however, will stand by his deputy's views, said Stephane Dujarric, the UN chief spokesman.
"There is no question of any action to be taken against the deputy secretary-general," he said.
Malloch Brown had said in a speech to a political conference in New York on Tuesday that the US used the UN "almost by stealth as a diplomatic tool while failing to stand up for it against its domestic critics".
The US government looked for UN support to deal with conflicts around the world while failing to defend it from conservative critics at home, Malloch Brown said.
"The UN's role is, in effect, a secret in middle America even as it is highlighted in the Middle East and other parts of the world," he said.
The speech brought an angry response from Bolton, who accused Malloch Brown of employing "a condescending, patronising tone about the American people".
Brown said later that his remarks were a "constructive critique of US policy towards the UN by a friend and an admirer".
Malloch Brown was named deputy secretary-general in March after serving as Annan's chief of staff and head of the UN development programme.