Democrats on Capitol Hill are putting pressure on Deutsche Bank to hire an independent auditor to review private accounts held by Donald Trump and his family, in order for Congress to determine whether the US president has financial ties to Russia.

Maxine Waters, the top ranking Democrat on the House financial services committee, also said she wanted Deutsche to hand over all communication and documentation relating to the underwriting of loans made to Trump and his immediate family members, including all assets and guarantees that were used to collaterise the loans.

Deutsche extended about $300m in loans to Trump before he became president, even as the former reality television star and businessman was being shunned by other financial institutions because of his poor track record and string of failed businesses.

The FBI is investigating possible collusion between members of the Trump campaign and the Kremlin following an assessment by US intelligence agencies that Russian state actors interfered in the US election. Trump’s finances are not believed to be at the centre of the probe, but a unit of the US Treasury that specialises in combatting money laundering is expected to share financial records sought by the Senate intelligence committee in their probe of possible Russian collusion, according to a recent report in the Wall Street Journal.

Waters’ letter to Deutsche chief executive John Cryan is not likely to force the German bank’s hand because Democrats do not have the power to compel a response. But the letter from a powerful voice on Capitol Hill underscored that the bank, which counts Trump, his daughter Ivanka and her husband Jared Kushner, and Kushner’s mother as clients, remains in the crosshairs of Democrats in Congress. It is also under a continuing investigation by the Department of Justice and is believed to be negotiating a settlement on allegations that are unrelated to the Trump administration.

Democrats in the House have also written to the US treasury secretary, Steve Mnuchin, demanding that his department hand over “all records of loans, guarantees, or other forms of credit” that have been extended to Trump and passed through Russia. It also sought more information on allegations that gambling casinos once owned by Trump were used to launder illicit funds. Among other requests, the letter also asked Mnuchin to hand over information about possible Russian involvement in any Trump-branded businesses.

The request came after an article recently emerged that showed one of Trump’s sons, Eric, told Golf writer James Dodson in 2014 that Trump’s golf courses relied on Russian money because of tight financing.

“We don’t rely on American banks. We have all the funding we need out of Russia,” Eric reportedly told Dodson.

Pressed to explain, Eric reportedly added: “We’ve got some guys that really, really love golf, and they’re really invested in our programs. We just go there all the time.”

The Democrats’ letter to Deutsche Bank, which was signed by top Democrats who sit on the House financial services committee, pointed to a “troubling” lack of transparency about a handful of controversies that have hit the German bank. It singled out a Russian mirror trading scheme at Deutsche’s former Moscow branch that allegedly allowed $10bn to flow out of Russia. It is still unclear who benefited from the scheme, the letter said.

“Likewise, Congress remains in the dark on whether loans Deutsche Bank made to President Trump were guaranteed by the Russian government, or were in any way connected to Russia,” the Democrats said.

They also wanted more information on a scheme knows as “The Russian Laundromat”, in which $20bn of funds originating in Russia were processed through dozens of banks.

Deutsche Bank declined a request to comment.

• This article was amended on 24 May 2017 to clarify that not all Democrats on the committee signed the letter.