The 99 Problems hitmaker and West teamed up for 2011 album Watch The Throne, but fell out after Jay Z refused to include two tracks on the collaborative project as he had them earmarked for his new offering.
Jay Z recorded the pieces - Holy Grail and Oceans - and played them to West, who was adamant they should feature on their joint album, and relations between the pair became tense after they struggled to reach a decision.
Jay Z tells Britain's BBC Radio 1, "We had this whole plan when me and Kanye did (the) Watch The Throne album that we would go right into our solos after that. Soon as I thought we had wrapped up Watch The Throne, I made two records - I had Holy Grail and Oceans.
"(There were) no lyrics on Holy Grail and I recorded Oceans and I played those records for Kanye. And he was like, 'No those have to go on Watch The Throne', so we spent four days arguing about those records and I was explaining to him why it wasn't right for this project and I had a whole idea for making this album called Magna Carta Holy Grail (part of) the name came after."
However, Jay Z insists the argument never really turned nasty, describing it as "four days literally arguing... not like fighting".
He adds, "Well, there was some pushing at one point but not between us, just everyone else got a little excited."
Magna Carta Holy Grail is Jay Z's 12th studio offering and it landed him his first U.K. number one on Sunday (14Jul13).
The interview, with BBC Radio 1 show host Zane Lowe, will be broadcast in four parts from Monday to Thursday this week (15-18Jul13).