Elliott's agent said Tuesday that his client thought Jones's "Zeke who?" joke was disrespectful.
Jerry Jones believes he has "earned the right" to joke with running back Ezekiel Elliott.
Speaking to reporters on Tuesday, Jones responded to the backlash he received from Elliott and his agent following his "Zeke who?" quip over the weekend.
"I've earned the right with Zeke to joke, period," Jones said. "I've earned it."
On Monday, Elliott's agent Rocky Arceneaux said neither he nor his client was amused by Jones's joke, which was made on Saturday after rookie Tony Pollard impressed during the Cowboys' preseason game against the Rams.
"I didn't think it was funny and neither did Zeke—we actually thought it was disrespectful," Arceneaux told ESPN.
Elliott is still training in Cabo San Lucas amid his ongoing contract holdout with the Cowboys, which began at the start of training camp. He is under contract through 2020 and is set to make $3.85 million in 2019 and $9.1 million in 2020 if he doesn't receive a new deal.
The Cowboys were informed by Elliott's representatives last week that their All-Pro running back will not play in 2019 without a new contract.
Jones said Tuesday that the two have not spoken since the comment was made on Saturday.
Elliott leads the NFL with 4,048 rushing yards since joining the league in 2016. The Cowboys won the NFC East in 2018 at 10–6.