Banks have made major progress when it comes to promoting gay and lesbian equality and diversity at home. Now their main problems are abroad.

For the biggest financial companies, the past year has tested their recent commitment to equal rights everywhere that they do business. Countries including Russia, Uganda and Brunei have recently passed harsh anti-gay laws, making homosexuality punishable by jail time and even death.

Those laws are challenging the policies — and the generally glowing reputations — that big multinational companies have established for promoting and protecting homosexual equality in recent years. Financial companies including Visa (NYSE:V) and Citigroup (NYSE:C), for example, recently drew scrutiny and some protests for sponsoring the Sochi Olympics and doing other business in Russia while not explicitly condemning the country's anti-gay laws.

Top executives at some of those companies acknowledged the problems on Thursday, while professing their ongoing commitment to gay rights.

"There's a lot of grey in the world. We have to be mindful of the rules and laws in the places where we operate," Michael Corbat, the chief executive of Citigroup (NYSE:C), said during a panel discussion at his company's downtown investment bank offices.

Corbat argued that companies such as Citigroup, which regularly touts its "global" presence and operations in more than 100 countries, can advocate for change in those countries — but can do so more effectively in private than in public.

"You can't run from these places. … You've got to work behind the scenes," he said, adding that "behind the scenes, we will use all our resources to have the conversation" about why laws criminalizing homosexuality are wrong.

He didn't provide many specifics about what exactly Citigroup is doing behind the scenes in places like Russia to advocate for change to its anti-gay laws. The bank is cutting back on the assets it has in that country after its invasion of Crimea, due to "ongoing political tensions in Russia and the Ukraine," Citi said in a regulatory filing Friday.

MasterCard (MA) is another company that has seen its business buffeted by the international political tensions surrounding Russia. But at the same panel discussion on Thursday, CEO Ajay Banga agreed with Corbat's strategy in advocating for change to anti-gay laws there and elsewhere abroad.

Big financial companies should "start from the logic of arguing for equality … then you can start tackling issues one by one," Banga said.

He and Corbat were speaking at the annual "Out on the Street" conference in New York, an event devoted to lesbian, gay, bisexual and transgender equality on Wall Street.

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