Kontos, who's arbitration-eligible for the first time, filed for $1.35 million, up from the $517,500 he earned last year. The Giants offered him $850,000.
Negotiations are expected to continue until a hearing before an arbitration panel is held between Feb. 1-21. At the hearing, each side presents its case to the panel, which selects one of the salary figures.
"I've worked well with these agents on many other deals, and I anticipate we'll roll up our sleeves and do the best we can," Giants general manager Bobby Evans said. J.D. Smart of Excel Sports Management represents Belt, while Sam Levinson of ACES negotiates for Kontos.
Belt batted .280 in 137 games, and he established career highs with 18 homers and 68 RBIs in 2015. Kontos appeared in a career-high 73 games and recorded a personal-best 2.33 ERA last year.
Chris Haft is a reporter for MLB.com. Read his blog, Haft-Baked Ideas, follow him on Twitter at @sfgiantsbeat and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.