Mr Singh begged the 50-year-old actor not to delete a song he recorded for Mr Khan's new film Sultan, the trailer of which was released on Tuesday. Arijit Singh, known for his work in films like Aashiqui 2 and Dilwale, has not previously sung for Salman Khan.
In his note, Mr Singh says he has attempted to apologise to Mr Khan several times via text and in person and at 'Nita ji's' residence - presumably Nita Ambani but this is not clear. It's also not clear how Mr Singh insulted the Bajrangi Bhaijaan star, though there have been rumours that Salman Khan felt disrespected by Arijit Singh at a musical gala.
The singer has not yet deleted a second Facebook post in which he hopes to finally get through to Mr Khan but also predicts trouble.
Salman Khan's Sultan, in which he plays a Haryanvi wrestler and which co-stars Anushka Sharma, releases this July.
Here's the text of Arijit Singh's now-deleted Facebook apology:
"Dear Mr Salman Khan
This is the last way I thought I would speak to you. I have been trying to text you call you and do everything possible to tell you that you are mistaken about the fact that I insulted you. I never did. That night in the show It was the wrong time and wrong aura.
Nevertheless you felt insulted.
And I understood and I felt extremely sorry about it as me and my family have been your fan since long. I tried to explain so many times but you never got it. I apologized but you never got it. How many times I sent you apology texts you also know.
At Nita Ji's place I only came back to apologize to you but you dint get it.
No problem I apologize here In front of everyone but please it is a request.
Please do not remove the song that I sang for you in Sultan. You want anyone else to sing this song, absolutely fine but keep a version at least. I have sung enough songs sir. But I want to retire with at least one song of you keeping in my library. Please do not take away this feeling.
I don't know why am I doing this I know the consequences
People are going to write their heart and mind and everything. I also know you won't be bothered Mr Salman Khan.
Still I think I need to take it out. After all I have to live with this fact that you made sure that I don't sing for you even though so many of us requested.
But I will be a fan bhaijaan..
Jagg ghumeya thare jaisa na koi..
Let there be light"
Arijit Singh made his debut as a singer in Bollywood with Phir Mohabbat from Murder 2 and has also sang for movies like Aashiqui 2,Dilwale, Airlift and Tamasha.
Salman Khan was last seen in 2015's Prem Ratan Dhan Payo and stars as a Haryanvi wrestler in Sultan which also features Anushka Sharma. Sultan releases on Eid this year.