Graphic showing facts on cholera, which causes up to 120,000 deaths worldwide each year
The 65,000 new cases reported in 2013 were the lowest reported yet but still more than 550 people died, according to UN figures.
Medrano said that unless funds are found the UN estimates that the number of cases could double this year and deaths increase four fold.
"If we are not prepared to make the investment now, we will have this year perhaps close to 180,000 cases and even up to 2,000 fatalities," he said.
The strain of cholera, that originally came from South Asia, has already been reported in Mexico, Cuba and Dominican Republic with some deaths.
A single case of cholera in a Peruvian port in the 1990s spread to 18 South American countries and killed 10,000 people, Medrano noted.
The UN assistant secretary general, who was named to the tough post in October, called for "a Marshall Plan for water and sanitation" in Haiti, a country of 10 million people with a long history of natural disasters and political strife.
Thony Belizaire, AFP/File
A Haitian man carries his ill mother on November 7, 2012 to the MSF(Doctors Without Borders) clinic in Delmas, Haiti, for treatment of Cholera
The UN has launched an appeal to raise $2.2 billion dollars for Haiti over the decade. But Medrano said $400 million has to be found over two years to contain the epidemic and build infrastructure to stop a repeat.
"This is a must and we can't wait 10 years to have the whole country covered. We need to have a massive investment in water purification, sanitation, toilets," he said.
The Haitian government has reported more than 680,000 cases since the epidemic broke out in October 2010 near a UN camp where Nepalese peacekeepers were based.
Lawyers from the US-based Institute for Justice and Democracy in Haiti (IJDH) filed a lawsuit in New York in October seeking compensation from the United Nations.
"We are in Haiti and our response to the cholera has nothing to do with the legal claim or because the UN is responsible or not responsible," said Medrano.
"We will have enough time in the future to discuss the cause. There will be a proper place to discuss that. Now we are concerned with the response because people are dying."
Thony Belizaire, AFP/File
Cholera patients are admitted to the MSF (Doctors Without Borders) clinic on November 7, 2012 in Delmas, Haiti
The envoy said many private aid groups had left Haiti because they have no cash. Many governments believe the emergency is finished and there are competing appeals for billions of dollars for Syria, Central African Republic, the Philippines and South Sudan.
Some 200 cholera treatment centres were set up as the epidemic spread. But Medrano said they are now under threat.
"If we have cholera treatment centres with no resources, understaffed, without money to pay staff, what are we going to do? People from remote areas are travelling to the treatment centre and it is closed -- lack of resources or they are dealing with NGOs who are no longer there."
Olivier Shulz, head of the Doctors Without Borders mission in Port-au-Prince, would not comment on predictions of increased fatalities but said prevention work was critical before the rainy season starts.
The group, which is virtually alone treating cholera patients in the capital, had to increase its staffing in Haiti last year because so many other groups left the country.
Now the MSF doctors and nurses are handling about 10 new cases a day. In the rainy season, this can increase to more than 100, Shulz told AFP.
"May comes very very quickly, the rains come very, very quickly and everyone scrambles to talk about prevention then," he said.