Latvia's anti-corruption agency says the criminal investigation against Mr Rimševics is not related to money-laundering accusations levelled against the country's third largest bank, ABLV, by the US Treasury.
The European Central Bank had earlier stopped all payments by ABLV, citing the sharp deterioration in its financial position in recent days and saying a moratorium was needed to allow the bank and Latvian authorities to address the situation. One bank, ABLV, has already needed a rescue loan from the central bank to remain afloat.
The U.S. Treasury Department has proposed sanctions against a major Latvian bank for alleged money laundering linked to North Korea's weapons program.
However, Latvia's relations with Russian Federation have been tense for several years.
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Prime Minister Maris Kucinskis sought to reassure the nation that the economy and the financial system were stable.
But Kucinskis also said that Rimsevics's case had no connection with the order imposed on ABLV.
Latvia's government took the relatively unusual step February 19 of issuing a set of English-language media bulletpoints in a clear attempt to dampen down the swirling global media speculation about the country's banking sector.
USA allegations that a leading bank engaged in money laundering and helped breach North Korean sanctions have also turned a spotlight on Latvia's financial system in recent days. Then why would commercial banks try to attack him?
He said his bank "still aims to find a win-win settlement with Latvia" in the arbitration process.
"We don't participate in any illegal activities", ABLV Bank Deputy CEO Vadims Reinfelds told a news conference.
Last week, the bank said the USA accusations were based on unfounded and misleading information.