MELBOURNE, Australia—Two of Australia’s largest banks admitted that several employees in Singapore tried to manipulate the benchmark rate for the Malaysian ringgit, although there is no evidence they were successful.

On Friday, Australia’s antitrust regulator began proceedings in federal court against Australia & New Zealand Banking Group Ltd. and Macquarie Group Ltd.The regulator claims the banks attempted to engage in cartel conduct.

The banks each confirmed they had agreed to settle with the regulator in relation to the conduct of employees in 2011. The identities of the individuals weren’t disclosed in statements from the banks and regulator.

The Australian Competition and Consumer Commission said it agreed with ANZ and Macquarie on facts that would be presented to the court for consideration, including that a Macquarie trader and traders employed by ANZ—along with a number of other unspecified banks in Singapore—had communicated in private online chat rooms about daily submissions to be made to the Association of Banks in Singapore regarding the ringgit fixing rate.

The banks and the regulator also agreed that on various dates in 2011, the traders tried to make arrangements with other banks that submitting banks would make high or low bids to the Association of Banks in Singapore. The ACCC alleges ANZ and Macquarie sought to influence the fixing rate.

ANZ said it agreed that three employees unsuccessfully attempted to influence the setting of benchmark rates used to settle contracts for the ringgit on 10 occasions. It agreed to a 9 million Australian dollar (US$6.7 million) penalty.

Macquarie, which agreed to pay a A$6 million penalty, said the regulator acknowledged that no senior manager or other employees were involved in or aware of the conduct of its junior employee in Singapore.

Macquarie said the employee was fired in 2012, while ANZ said the three employees that faced allegations are no longer employed by the bank.

The Association of Banks in Singapore’s benchmark rates are used as reference rates for settling non-deliverable forward contracts for currencies that aren’t freely tradable outside the domestic economy. Banks mainly use non-deliverable forward contracts for hedging and risk management.

The Australian regulator said ANZ was a submitting bank for the ringgit fixing rate, and Macquarie often initiated discussions between traders but wasn’t a submitting bank. It estimated that annual turnover for non-deliverable forward contracts in Australia was about A$9 million to A$10 million.

“These proceedings are a reminder that Australian cartel laws apply to financial markets and capture cartel conduct by firms that carry on business in Australia, regardless of where that conduct occurred,” ACCC Chairman Rod Sims said.

The federal court will determine if the penalties agreed upon with the regulator were appropriate. The ACCC said it wouldn’t comment further regarding penalties until the court made its final orders.

ANZ Chief Risk Officer Nigel Williams said the bank accepted responsibility and apologized for the actions of its former employees. He added that the matter was previously investigated by the Monetary Authority of Singapore, which completed a review and supervisory action in 2013 involving 20 banks operating in Singapore, but found no conclusive evidence that foreign exchange benchmarks had been successfully influenced.

Since that investigation, ANZ said it had strengthened its compliance systems. Similarly, Macquarie said it had tightened surveillance of electronic communications world-wide, improved trade monitoring and intensified training for its front office staff.

Write to Robb M. Stewart at robb.stewart@wsj.com