With fixtures coming thick and fast for Spurs, Mourinho had called on Southgate to protect Kane by not playing him in all of England's upcoming games, including a friendly with Wales and Nations League matches against Belgium and Denmark in October.
Southgate had hit back, saying concerns over Kane's fitness worked both ways. He urged Mourinho to ensure the England captain was in good shape for Euro 2020, which was postponed to next year due to the coronavirus outbreak.
Kane scored a hat-trick to guide the north London club into the Europa League group stage with a 7-2 win over Maccabi Haifa on Thursday - their third game in five days.
"This match was a fundamental match for us. A match that means a few million pounds and means that we are in a group phase of a competition that we have ambitions," Mourinho said.
"For my friend Gary, I can promise that until the end of the season I don't play Harry Kane one minute of any friendly match."
Spurs face Manchester United in the league on Sunday. (Reporting by Arvind Sriram in Bengaluru; Editing by Ana Nicolaci da Costa and Michael Perry)