Hallelujah, perhaps Cohen’s best-known work, was played twice during Thursday’s event, despite the estate saying they denied a request for its use.
A cover of the song played after President Donald Trump had delivered his speech, as fireworks erupted over Washington DC.
Michelle L Rice, the Cohen estate’s lawyer, said they are considering legal action as a result.
She said: “We are surprised and dismayed that the RNC would proceed knowing that the Cohen Estate had specifically declined the RNC’s use request, and their rather brazen attempt to politicise and exploit in such an egregious manner Hallelujah, one of the most important songs in the Cohen song catalogue. We are exploring our legal options.”
Rice added: “Had the RNC requested another song, You Want It Darker, for which Leonard won a posthumous Grammy in 2017, we might have considered approval of that song.”
Cohen’s publishing company Sony/ATV Music Publishing also confirmed they had been approached by representatives of the Republican National Committee and declined their request to use Hallelujah.
Brian J Monaco, president and global chief marketing officer, said: “On the eve of the finale of the convention, representatives from the Republican National Committee contacted us regarding obtaining permission for a live performance of Leonard Cohen’s Hallelujah. We declined their request.”
This is not the first time Mr Trump has found himself at odds with musicians over the unauthorised use of music.
At the 2016 Republic National Convention, the then presidential nominee was criticised by rock band Queen after using their anthem We Are The Champions.
The Tom Petty estate, the Rolling Stones and Neil Young have all objected to their music being used by Mr Trump.