The 33-year-old striker's LA Galaxy manager Bruce Arena had asked that the striker be withdrawn from the team to face Kazakhstan in Dublin on Tuesday evening.
However, King politely declined and Keane, who missed training on Wednesday morning with an ankle injury, will remain with his international team-mates for the duration.
A Football Association of Ireland statement said: "The Football Association of Ireland today confirmed that Noel King has responded this afternoon to the manager of LA Galaxy Bruce Arena to inform him that he has decided not to release Robbie Keane and trusts that he understands the position, having been an international manager himself.
"Bruce Arena had requested that the release of Robbie Keane be considered after the Germany match and before the international match against Kazakhstan in Dublin on 15 October."
The Republic of Ireland have only a mathematical chance of making the play-offs for next summer's finals in Brazil after defeats by rivals Sweden and Austria last month.
Keane, the Republic's record goalscorer with 60, will take his tally to 131 senior caps if he plays in both games.