"The month was the warmest June globally at just over 0.5 degrees Celsius above the 1991-2020 average, exceeding June 2019 - the previous record - by a substantial margin," the E.U. monitor said in a statement from its C3S climate unit.
Temperatures reached June records across northwest Europe while parts of Canada, the United States, Mexico, Asia and eastern Australia "were significantly warmer than normal", Copernicus noted.
On the other hand it was cooler than normal in western Australia, the western United States and western Russia, it said.
It was the latest in a series of heat records over recent years, reflecting the impact of global warming driven by greenhouse gases released from human activity.
For June, Copernicus noted that sea surface temperatures were higher globally than any previous June on record, with "extreme marine heat waves" around Ireland, Britain and the Baltic.
Antarctic sea ice reached its lowest extent for June since satellite observations began, at 17 percent below average.
C3S scientist Julien Nicolas told AFP the June record was driven largely by "very warm ocean surface temperatures" in the Pacific and Atlantic due to El Nino, a periodic warming phenomenon.
"On top of that is this warming trend of the ocean absorbing 90 percent of heat released by human activity," he added.
The global temperature was 0.53 C above the 30-year average at an average of 16.51C, he calculated.
"June 2023 is way above the others. This is the kind of anomaly we are not used to," Nicolas said.
Petteri Taalas, secretary-general of the UN's World Meteorological Organization, warned on Monday that El Nino "will greatly increase the likelihood of breaking temperature records and triggering more extreme heat in many parts of the world and in the ocean."
El Nino is a naturally occurring pattern that drives increased heat worldwide, as well as drought in some parts of the world and heavy rains elsewhere.
He urged governments "to mobilise preparations to limit the impacts on our health, our ecosystems and our economies."
As well as withering crops, melting glaciers and raising the risk of wildfires, higher-than-normal temperatures also cause health problems ranging from heatstroke and dehydration to cardiovascular stress.