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Lawyers seeking compensation for Haitians killed or sickened by cholera that they blame on United Nations peacekeepers said the U.N.'s admission on Thursday of its possible involvement in the outbreak was a breakthrough in their legal battle.

Human rights lawyers from the Boston-based Institute for Justice and Democracy in Haiti (IJDH), filed a lawsuit in November 2011 against the United Nations demanding a public apology and compensation on behalf of 5,000 cholera victims.

They say U.N. peacekeepers were responsible for introducing a cholera epidemic in Haiti in October 2010, following the massive earthquake that hit the impoverished Caribbean nation.

Cholera, a water-born disease, which continues in Haiti today, has killed more than 9,000 Haitians and infected over 770,000 since the cholera outbreak began, U.N. figures show.

The U.N. had denied any responsibility or involvement in causing the cholera outbreak, lawyers say.

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But in response to reporters' questions on Thursday, Farhan Haq, spokesman for U.N. Secretary-General Ban Ki-moon said: "... over the past year the U.N. has become convinced it needs to do much more regarding its own involvement in the initial outbreak and the suffering of those affected by cholera."

Lawyers said the remarks were a victory for victims of cholera in Haiti.

"This is a groundbreaking first step towards justice," Beatrice Lindstrom, a lawyer at IJDH, told the Thomson Reuters Foundation in a telephone interview.

"Up until now, the U.N. had refused to engage in any kind of conversation about their role in the cholera outbreak. It is still, though, far from being a formal apology."

An independent panel appointed by U.N. chief Ban to study the epidemic did not determine conclusively how cholera was introduced to Haiti.

Its May 2011 report concluded that while the cholera bacteria did not originate "from the native environs of Haiti", the outbreak was "not the fault of, or deliberate action of, a group or individual."

However, a June 2011 study by the U.S. Centers for Disease Control and Prevention said U.N. peacekeepers from Nepal, where cholera is endemic, were the likely cause of the outbreak. The peacekeepers were stationed near a river and discharged raw sewage.

The lawsuit filed by IJDH lawyers was rejected by the U.N. in 2013.

In response, the rights group filed a class action lawsuit in a federal court in New York. But in January 2015, a judge dismissed the lawsuit saying the U.N. has legal immunity that only it can waive.

Lawyers then appealed the ruling and are now awaiting a decision from the court.

"We will continue to fight to get financial compensation for cholera victims, a formal public apology that victims are demanding and ensure the U.N. does much more to support water and sanitation efforts to eradicate cholera in Haiti," Lindstrom said.

If the judges deny the appeal, Lindstrom said they would seek to bring the case before the United States Supreme Court.

Health experts say cholera, which had not been documented in Haiti in almost 100 years prior to the outbreak, will continue to kill and infect Haitians as long as they lack access to clean water and sanitation.

Since the outbreak began in 2010, the U.N. has said it has worked to tackle cholera in Haiti and the neighboring Dominican Republic, through a multi-billion donor aid program to improve sanitation and an oral vaccine program against cholera.

The U.N. has struggled to raise donor funds to eradicate cholera as part of a 10-year program. Less than a quarter of the $2.1 billion the U.N. is seeking has been raised so far, U.N. figures show.

Haq said the U.N. would announce a "new response" to tackling cholera in Haiti within the next two months.