The ICCO daily price averaged $2,017 (€1484) per tonne, up by $12 (€8.8) on May's monthly average, and ranged between $1,923 (€1415) and $2,143 (€1,576) per tonne.
The report said the high prices were due to the uncertain outlook for the cocoa market due to recent supply problems, causing prices to reach their highest since 2003, and increasing costs for processors.
"Market participants were still focusing on the situation of the 2006/07 cocoa season with its large production deficit and below than usual forward price coverage held by cocoa processors and chocolate manufacturers."
Prices reached £1,110 (€1626) per tonne on the London market and $2,065 (€1519) in New York.
Prices seemed to slow down on June 7 and 8, which the report said was due to the strengthening of the dollar against other currencies.
The reason behind this continued rise in prices and market uncertainty is due to the current global deficit of 145,000 tonnes of cocoa forecast this season by the ICCO.
This is compared to the 192,000 tonne surplus in the 2005-2006 season.
This report comes as both Indonesia and Ghana, two of the world's largest cocoa producers, announced in June that they both expect production to rise over the next few years.
Indonesia, the world's third largest cocoa producer, said it hoped to raise the country's cocoa production from 590,000 tonnes a year to one million tonnes by 2012.
Halim Abdul Razak, chairman of the Indonesian Cocoa Association (Askindo), said, "the world's increasing demand for cocoa at present serves a good condition for increasing the country's cocoa productivity."
The same week, Ghana announced it wanted to boost its output to one million tonnes by 2010.
Ghana currently produces 650,000 tonnes of cocoa as the world's second largest cocoa producer after Ivory Coast.
However, the ICCO predicts a promising outlook to the 2007/08 season due to current rainfall encouraging crops to come early, and perhaps even early enough to be counted within the 2006/07 season, ultimately increasing the size of the current season's production.
The report also expects Ghanaian farmers to store beans harvested in September until October, the official start of the new season, due to the expectations of higher prices.
This, however, would mean early crops may not be counted in the 2006/07 season, and cocoa deficit will remain low.
"So far, there is no consensus among market participants on the direction of cocoa prices during the summer.
The strong increase in June prices reflected that market participants were still focusing on the 2006/2007 cocoa season."