“Our currency is our credibility,” said Frederick Kempe, chief executive of the Atlantic Council, a fast-growing research center that focuses mainly on international affairs and has accepted donations from at least 25 countries since 2008. “Most of the governments that come to us, they understand we are not lobbyists. We are a different entity, and they work with us for totally different purposes.”

In their contracts and internal documents, however, foreign governments are often explicit about what they expect from the research groups they finance.

“In Washington, it is difficult for a small country to gain access to powerful politicians, bureaucrats and experts,” states an internal report commissioned by the Norwegian Foreign Affairs Ministry assessing its grant making. “Funding powerful think tanks is one way to gain such access, and some think tanks in Washington are openly conveying that they can service only those foreign governments that provide funding.”

The think tanks’ reliance on funds from overseas is driven, in part, by intensifying competition within the field: The number of policy groups has multiplied in recent years, while research grants from the United States government have dwindled.

Foreign officials describe these relationships as pivotal to winning influence on the cluttered Washington stage, where hundreds of nations jockey for attention from the United States government. The arrangements vary: Some countries work directly with think tanks, drawing contracts that define the scope and direction of research. Others donate money to the think tanks, and then pay teams of lobbyists and public relations consultants to push the think tanks to promote the country’s agenda.

“Japan is not necessarily the most interesting subject around the world,” said Masato Otaka, a spokesman for the Japanese Embassy, when asked why Japan donates heavily to American research groups. “We’ve been experiencing some slower growth in the economy. I think our presence is less felt than before.”

The scope of foreign financing for American think tanks is difficult to determine. But since 2011, at least 64 foreign governments, state-controlled entities or government officials have contributed to a group of 28 major United States-based research organizations, according to disclosures by the institutions and government documents. What little information the organizations volunteer about their donors, along with public records and lobbying reports filed with American officials by foreign representatives, indicates a minimum of $92 million in contributions or commitments from overseas government interests over the last four years. The total is certainly more.