Last month smashed the previous record for April by the largest margin ever, the data show.
That makes it three months in a row that the monthly record was broken by the largest margin ever.
But in terms of its departure from the 1951-1980 temperature average used by Nasa, April was equal with January 2016.
February and March this year showed greater departures from the norm.
The new record for April trounced the previous one, set in 2010, by 0.24C.
"The very unfortunate circumstance we have now is the overlap of a very intense El Nino that has been magnified by climate change," said Christiana Figueres, executive secretary of the UN Framework Convention on Climate Change.
"All of these record breaking temperatures and attendant implications that we have had, such as record breaking fires for example, and droughts in India are all reminders that we cannot afford to do anything except to accelerate the solution agenda - we absolutely have no other option but to accelerate."
Gavin Schmidt, director of the Nasa Goddard Institute for Space Studies, which analyses global temperature datasets, tweeted: "With Apr[il] update, 2016 still (greater than) 99% likely to be a new record (assuming historical ytd [year-to-date]/ann[ual]patterns valid)."
Several northerly regions, including the US state of Alaska, saw very hot temperatures during April - a pattern repeated in previous months.
The records for April will also raise questions about the achievability of a goal to hold global warming to 1.5C that was agreed at the Paris climate talks in December 2015.
April breaks global temperature record
17 May 2016
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April was the seventh month in a row that broke global temperature records, Nasa figures show.
