Romy Andrianarisoa, 46, the top aide to Madagascan President Andry Rajoelina, and Philippe Tabuteau, 54, are accused of seeking a bribe from a British mining company to secure licences to operate in Madagascar.
The pair were remanded in custody on Saturday after they were arrested Thursday in central London "at a meeting where they are suspected of having attempted to solicit a bribe," the NCA said.
"Following a fast-paced investigation into suspected bribery in action, Andrianarisoa and Tabuteau were arrested in the Victoria area of London on Thursday afternoon," it added.
They are next set to appear in court in south London on September 8.
The NCA, which targets serious and organized crime in Britain and internationally, said its probe began after the mining firm, Gemfields, "raised concerns" with the agency.
Andrianarisoa and Tabuteau, a French national, were seeking around £225,000 ($285,000) in "upfront charges," as well as a 5% equity stake in a proposed license deal on the island nation off the southeastern coast of Africa, it said.
No further details about the alleged offenses were provided.
Andy Kelly, head of the NCA's international corruption unit, praised Gemfields for "bringing this matter to our attention and for their ongoing cooperation with the investigation."
"Their quick reactions to engage the NCA have been critical to our ability to pursue this case," he added.
The pair were each charged with one count of requesting, agreeing to receive or accepting a bribe, under Britain's 2010 Bribery Act.
If convicted, they could each face up to 10 years in prison.
Gemfields, which mines and markets colored gemstones, specializes in emeralds mined from Zambia and rubies from Mozambique, according to its website.
It does not currently operate any mines in Madagascar but owns Madagascar-based Oriental Mining, which does reportedly hold licences to mine there.
Gemfields did immediately respond to a request for comment by AFP.