The US National Oceanic and Atmospheric Administration (NOAA) said the average global temperature was 1.7F warmer than the 20th Century average.
The heat was most notable in parts of Europe, Russia, Canada and South America, it said.
The NOAA report was released as the US prepares for a "dangerous heatwave".
The National Weather Service has warned that tens of millions of people will be affected by excessive heat in the coming days, with temperatures expected to reach up to 110F (43.3C).
"Friday is going to be bad. Saturday is going to be really, really bad," New York Mayor Bill de Blasio said in a video posted on Twitter on Thursday. "Take it seriously."
In its latest monthly global climate report, the NOAA said the heat in June had brought Antarctic sea ice coverage to a record low.
Nine of the 10 hottest Junes on its 1880-2019 record have occurred in the past nine years, it said. Last month beat June 2016 to be named the hottest.
Nasa and other groups also reached the same conclusion last month.
Scientists have warned that record-setting temperatures will continue as a result of climate change.
"Earth is running a fever that won't break thanks to climate change," climatologist Kathie Dello told the Associated Press news agency. "This won't be the last record warm summer month that we will see."
More about: climate-change