Richards went 15-12 with a 3.65 ERA for the Angels the past season. He also shined in 2014, his first year as a regular big league starter, as he went 13-4 with a 2.61 ERA before a season-ending knee injury.
The Angels offered $5.3 million last week, and Richards countered with $7.1 million. He made $3.2 million last year.
Richards won't be a free agent until after the 2018 season.
Gold Glove right fielder Kole Calhoun is the Angels' only remaining arbitration-eligible player.