Detroit made the offers to pitcher Max Scherzer and first baseman-designated hitter Victor Martinez, and Pittsburgh to left-hander Francisco Liriano and catcher Russell Martin.
Also receiving offers were shortstop Hanley Ramirez (Los Angeles Dodgers), outfielder Nelson Cruz (Baltimore), right-hander James Shields (Kansas City), closer David Robertson (New York Yankees), outfielder Melky Cabrera (Toronto), pitcher Ervin Santana (Atlanta) and outfielder Michael Cuddyer (Colorado).
An offer could be made only to a free agent who was with the team for the entire season, and players have until Nov. 10 to accept. The price was determined by the average of the top 125 major league contracts this year by average annual value.
If a player rejects a qualifying offer and signs a major league contract with another club before the June amateur draft, his former team would receive a draft pick as compensation at the end of the first round.
The club signing that player loses its first-round pick in the amateur draft, unless that pick is among the top 10, in which case the club signing that player loses its next-highest pick.
None of the 22 qualifying offers made after the past two seasons was accepted.
A total of 137 players became free agents, and 136 can start negotiating money with all teams starting Tuesday. Reliever Koji Uehrara agreed last week to stay with Boston for an $18 million, two-year deal.
Three players who potentially could have become free agents stayed with their teams. Third baseman Aramis Ramirez exercised his half of a $14 million mutual option with Milwaukee; left-hander Tsuyoshi Wada agreed to a $4 million, one-year contract with the Chicago Cubs; and Tampa Bay exercised a $2.5 million option on right-hander Joel Peralta.
Pitcher A.J. Burnett declined a $12.75 million player option to return to Philadelphia. Burnett and Baltimore catcher Nick Hundley became the final free agents.
Kansas City exercised a $7 million option on reliever Wade Davis, who would have been eligible for salary arbitration.