The UN is facing claims for hundreds of millions of dollars in compensation from Haitian cholera victims.
Several studies have found that cholera was probably brought to Haiti by UN peacekeepers from Nepal.
The US-based Institute for Justice and Democracy in Haiti filed the demand on behalf of some 5,000 victims.
It says the UN mission in Haiti failed to screen peacekeepers for cholera and allowed untreated waste from a UN base to be dumped into the main river.
It also says the UN mission failed to respond adequately to the outbreak.
The demand would be looked at by the "relevant parts of the UN system", spokesman Martin Nesirsky said.
The UN was working "to do everything possible to bring the spread of cholera under control, to treat and support those affected by cholera and ultimately to eradicate cholera from Haiti," he said.
More than 6,500 Haitians have died of cholera since the outbreak began in October 2010, according to the Haitian Ministry of Health, and nearly 500,000 have been made ill.
The Institute for Justice and Democracy in Haiti (IJDH) - a Boston-based human rights group - is demanding $50,000 (£31,000) in compensation for each sick person and $100,000 (£62,000) for each death.
As well as individual damages, it also wants a public apology and an adequate nationwide response - including medical care, clean water and sanitation infrastructure.
The group says it is prepared to go to court in Haiti or the US if the UN does not respond.
"It is time for the UN to step up and do the right thing," IJDH director Brian Concannon said.
"The majority of our petition's facts come from UN reports. The UN developed much of the law we cite," he said.
"Our clients are challenging the institution to act consistently with what it knows to be true and just".
A UN report on Haiti's cholera epidemic - drawn up by by independent experts and published in May - found that the outbreak was the result of a "confluence of circumstances" rather than the fault of a group or individual.
But it strongly suggested that the disease was introduced by UN peacekeepers from Nepal living on a base where poor sanitary conditions allowed human waste to enter the Artibonite river system.
A report by the US Center for Disease Control also linked the outbreak to Nepalese troops.
The cholera epidemic provoked widespread demonstrations against the UN mission, which has been in Haiti since 2004.
Haitians have little natural resistance to cholera, and the waterborne disease spread rapidly in a country whose already poor infrastructure was shattered by the January 2010 earthquake.