The criticism from Senator Bob Corker, a Republican who chairs the Senate Foreign Relations Committee, comes as candidates to replace Ban when he leaves the post at the end of the year after 10 years have been holding town hall meetings with diplomats from UN member states this week.
Ending UN peacekeeper abuse has been a major topic of discussion during the meetings at UN headquarters in light of a slew of rape allegations leveled against international peacekeepers in Central African Republic.
Corker asked a committee hearing on ending sexual abuse by UN peacekeepers why some recommendations included in a 2005 report on the problem to the UN General Assembly were only now being implemented.
"What is wrong with the secretary-general of the UN?" Corker asked at the hearing, which was broadcast live. "This report ... the one that you refer to, is 10 years old."
"How do we put up with such inept leadership at the United Nations?" he said, adding that he was "disgusted" by the abuse.
UN spokesman Stephane Dujarric said Ban was "determined to continue to shine a spotlight on the scourge of sexual exploitation and abuse by peacekeepers and hold those responsible accountable."
"However, this is a fight that no one person can lead alone," Dujarric added. "Member states are the only ones who have the power to swiftly bring to justice those who have committed crimes and to impose the strongest possible disciplinary and criminal sanctions."
Ambassador Isobel Coleman, who oversees UN management and reform issues at the US mission to the United Nations, said countries that contribute UN troops were often unwilling to hold those who commit abuses accountable.
"I don't think it's ineptitude," Coleman said. "I think it is a reluctance to take on the opposition of troop contributing countries that don't want to deal with this issue in the transparent way that it must be dealt with."
She added that the United States was monitoring follow-up actions in troop-contributing countries to ensure people accused of sexual abuse are prosecuted.
Republicans are traditionally more critical of the United Nations than Democrats. The United States contributes 27 percent of the UN's $8.3 billion peacekeeping budget.
Ban has pushed the UN to "name and shame" countries whose troops are accused of sexual abuse. Some 800 Congolese peacekeepers were repatriated earlier this year over alleged sex crimes.
In December, an independent review panel accused the United Nations and its agencies of grossly mishandling allegations of child sexual abuse by international peacekeepers in Central African Republic in 2013 and 2014.