Mihails Ulmans and his associate, co-defendant Aleksandrs Babenko, are alleged to have paid the killer of insolvency lawyer Martins Bunkus.
Mr Bunkus is said to have uncovered evidence of money-laundering at LPB bank, partly owned by Mr Ulmans.
He was shot dead in 2018. Both defendants deny any involvement.
According to prosecutors, Mr Bunkus came across evidence that the two men were involved in money-laundering while he was winding up another firm. He then took his concerns to Latvian financial crime watchdogs.
Mr Bunkus suffered one unsuccessful attempt on his life in September 2016, but was then shot dead in broad daylight with an assault rifle in rush-hour traffic in May 2018.
Police reports say his attackers had secreted a Kalashnikov rifle under a tent on a cargo trailer, which they towed behind a van. At least seven rounds of ammunition were fired into Mr Bunkus’s car.
Mr Ulmans and Mr Babenko were arrested in connection with the crime in May 2022, four years after it took place. They have been in custody ever since.
Mr Babenko’s lawyers say his rights have been violated by being kept in custody for so long.
The prosecution alleges that €100,000 (£86,850) was promised to the person who arranged Mr Bunkus’s murder and €200,000 to the killer.
A third man, a Russian national, is on trial accused of carrying out the murder.
The three men will be tried by a judge without a jury, as is common practice in Latvia.
As well as his part-ownership of LPB, Mr Ulmans has investments in various other business sectors, including duty-free shops in Russian airports, as well as customs warehouses.
It is not the first time that allegations of money-laundering in the Latvian banking system have surfaced.
The country’s third-largest bank, ABLV, went into voluntary liquidation in 2018 after the US Treasury accused it of a wide range of offences including sanctions breaches.
In the same year, LPB itself was fined €2.2m (£1.9m) for failing to resolve regulatory problems dating back to 2016.
Latvia has since introduced wide-ranging reforms in an effort to stop the flow of tainted money, mainly from Russia.