Visa and Mastercard executives met members of the Russian government in St Petersburg to discuss new rules that would oblige foreign card companies to pay a hefty security deposit to the central bank to work in Russia.
The companies said the rules - passed by Russia's parliament after the West imposed sanctions on a number of individuals and companies over the Ukraine crisis - would complicate their Russian operations but had no plans to exit.
"In any situation, we will stay in Russia," Ilya Ryaby, general director of Mastercard in Russia, told journalists at the St Petersburg International Economic Forum.
Andrew Torre, director of Visa in Russia, said: "We are willing to work in Russia and after this meeting we hope that a compromise solution will be found".
After Friday's meeting, Ryaby said the card companies had discussed what could be done to create a system of cashless transactions and a system of servicing payment cards in Russia.
Russian Finance Minister Anton Siluanov told reporters that Visa and Mastercard's plans to set up Russia-based subsidiaries would take around a year and a half. In the meantime they would work with Russia's existing payment systems, he said.
"We are willing to cooperate in this direction," Siluanov said. "I think we will find a solution that suits both Visa and Mastercard and the Russian Federation."
Visa and Mastercard stopped serving several Russian banks after the United States imposed sanctions over the annexation of Crimea in March.
Russia later launched a package of measures aimed at stimulating the creation of a Russian national payment system to reduce its reliance on Western companies.
Among those measures, foreign card companies would from July 1 have to pay a security deposit of 25 percent of their average daily turnover in Russia to the central bank once a quarter.