Jenkins said the matter was investigated fully by "internal and external resources."
"We believe our defense is strong, and we intend to defend robustly those allegations that were made against us," he said in an interview with " Closing Bell ."
"Obviously if we have made mistakes, if we have gotten things wrong, then we'll acknowledge that, we'll take the sanction, we'll learn and we'll move on but where we think we are on strong ground, then we will defend our position."
New York Attorney General Eric Schneiderman brought the lawsuit against Barclays in June, and last week he defended it in court documents filed in the case. He also reasserted allegations that Barclays employees misled clients about their exposure to high-speed and potentially predatory market participants.
Jenkins said he couldn't specifically address the ongoing litigation but said the bank "responded robustly to the allegations."
Barclays filed a motion to dismiss the lawsuit in July, stating, among other things, that the state mischaracterized the bank's practices.
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-CNBC's Kate Kelly contributed to this report.