In a letter on Friday, Enders defended the decision to report anomalies to UK authorities, which had triggered the probes, and said he and general counsel John Harrison had the board's backing to "lead us through the process of bringing this issue to closure".
The potentially lengthy investigations could however lead to "significant penalties" against Airbus, he said, according to a text obtained by Reuters.
Airbus declined to comment.
Enders wrote to staff as fresh reports emerged over a separate investigation into alleged fraud in the sale of Eurofighter combat jets to Austria in 2003.
Enders is among individuals placed under investigation in Austria over the case, which is also the subject of a lengthy probe in Germany. He has denied any wrongdoing and criticised the Vienna probe as an abuse of the legal system.
Munich prosecutors said on Friday they expected soon to complete their investigations into the $2 billion deal, but declined to comment on a report by German weekly Der Spiegel that they would file charges soon.
French publication Mediapart said on Friday a vehicle allegedly used to funnel payments in the Eurofighter case had also served as a conduit for wider payments to obscure jurisdictions. Such payments are being investigated in the investigation over Airbus's use of middlemen in foreign deals.
Airbus has denied any wrongdoing in the Austria case. It had no immediate comment on the Mediapart story.
Britain's Serious Fraud Office (SFO) launched a probe into the use of agents in commercial jet deals in 2016, followed this year by France's fraud police.
The SFO acted after Airbus alerted UK authorities to inaccurate statements it had itself made over several years on the use of intermediaries in applications for support for jetliner exports.
Airbus has meanwhile launched a sweeping internal investigation in the hopes of obtaining a deferred prosecution agreement from the UK, which could lead to a costly settlement such as one Rolls-Royce
The use of outside U.S. lawyers and robust questioning of staff has raised hackles inside the company and led to French media speculation of a backlash against German-born Enders.
But in the letter, Enders spoke of attacks by vested interests and urged staff to ignore "simplistic and nationalistic bluster" and to focus on industrial priorities.
He called on staff to support the top management and the board in tackling the compliance issues and predicted Airbus would emerge stronger from the affair.