Free agents John Lackey, Matt Holliday and Jason Bay were among the players who declined. They can continue to negotiate with their former clubs with no time restrictions for signing.
Pavano, 34 next month, provided the Twins with a late boost. Acquired from Cleveland in early August for a minor leaguer, he went 5-4 over 12 starts down the stretch and helped Minnesota win the AL Central.
Pavano was a bust with the New York Yankees, going 9-8 overall in four injury-plagued seasons before signing with the Indians. He went a combined 14-12 with a 5.10 ERA in 33 starts this year.
Betancourt became a key setup man for the NL wild-card Rockies after they acquired him from Cleveland on July 23. The right-hander was 3-1 with a 1.79 ERA for Colorado and finished 4-3 overall with a 2.73 ERA in 61 games.
The Rockies declined a $5 million option on Betancourt last month and he filed for free agency.
Soriano had 27 saves while going 1-6 with a 2.97 ERA in 77 games for Atlanta. His role for next year is still undefined because the Braves have signed free-agent closer Billy Wagner and reliever Takashi Saito since the season ended. Soriano cannot be traded before June 16 without his consent, according to baseball's labor contract.
Atlanta reliever Mike Gonzalez, who had 10 saves, didn't accept arbitration.
In all, 23 players were offered arbitration. The list included Wagner and Chone Figgins, who has a tentative deal with Seattle. Adrian Beltre, Ivan Rodriguez, Joel Pineiro, Jose Valverde and Mark DeRosa were among the other players who declined.
If Pavano, Betancourt or Soriano fail to reach a deal by Jan. 19, they would exchange proposed salaries with their teams for 2010. Hearings would be held the first three weeks of February.