"We believe we have been co-operating. We have robustly responded to the allegations against us, that's going through the courts, and this is the next phase," Jenkins told CNBC in an interview at the World Economic Forum in Davos Thursday.
On Wednesday, New York Attorney-General Eric Schneiderman said the bank had defied subpoenas for the two top executives running the division which oversees its controversial "dark pool". The attorney-general also named the executives - William White, head of electronic trading, and David Johnsen, head of product development- for the first time.
The probe into the dark pool - an electronic trading system where the size and price of orders are not revealed to other participants - looks into a shadowy area where high-frequency traders are alleged to benefit to the detriment of other investors.
"These issues are from the past and we want to deal with them in the right way. If we've done something wrong we'll admit to it take the sanctions. When we feel that we haven't, we're going to defend our position," Jenkins said.
"In the course of this year, we will be able to put some of these issues behind us."
Jenkins, who took over two years ago after a scandal over the bank's fixing of the key Libor interest rate led to the resignation of predecessor Bob Diamond, warned investors last year that the bank may have to pay out more than the £500 million set side to deal with fines over the currency trading "dark pool." He told CNBC he still doesn't have a increased ballpark figure for the settlement.