BUDAPEST, Sept 26 (Reuters) - A move by Russia’s International Investment Bank (IIB) to Hungary and Budapest’s decision to grant immunity to the bank’s employees have alarmed a group of U.S. Democratic Senators, who raised their concerns in a letter to the U.S. ambassador in Hungary.

In a letter dated Sept. 24 and posted on U.S. Senator Dick Durbin’s website, signed by several senators, they asked Ambassador David Cornstein if Hungarian intelligence services had cooperated with U.S. intelligence in monitoring the activities of the IIB and its personnel now in Hungary.

The Hungarian government effectively has granted IIB directors and staff diplomatic immunity. The bank also is not subject to any regulatory supervision in Hungary.

Hungarian Prime Minister Viktor Orban, whose close ties with China and President Vladimir Putin’s Russia have drawn criticism from international partners, has said he wanted to build better ties with all major powers. Putin is due to visit Budapest on Oct. 30.

U.S. President Donald Trump praised Orban for his tough stance on immigration, calling him his “twin” in a bilateral meeting earlier this year.

“Several of us have written to you before about upholding American democratic values and security interests when dealing with the autocratic host government of Viktor Orban, whose embrace of Russia and antidemocratic actions are cause for considerable concern,” the senators wrote in the letter.

They said they were “deeply troubled” that Hungary proposed moving Russia’s IIB which is “widely seen as an arm of Russia’s secret services and whose chairman has longstanding ties to Russian intelligence – from Moscow to Budapest.”

“The relocation of the IIB has direct implications for U.S. national and NATO allies,” they said.

Orban’s ruling Fidesz party, at the proposal of the finance minister, passed an agreement in parliament in March with the IIB, setting out the conditions of the relocation of the bank to Budapest.

Under the deal, the government recognised the “international legal personality” of the IIB, giving its directors and staff diplomatic immunity. The bank is not subject to any financial or regulatory supervision or control in Hungary.

The IIB press office said in a reply to Reuters questions that it had around 50 international staff at its Budapest headquarters right now.

“The Bank will not provide any commentary on internal affairs of a non-member country. And that is exactly what the mentioned letter is,” the IIB added. It also said its privileges were “absolutely identical for every multilateral development bank in the world.”

A US embassy spokesperson said: “We do not comment on correspondence between members of Congress and the Department of State.” (Reporting by Krisztina Than, editing by Larry King)