(CNN) Top Republicans on Capitol Hill have made a concerted decision in their Russia inquiries: They are staying away from digging into the finances of President Donald Trump and his family.

Six Republican leaders of key committees told CNN they see little reason to pursue those lines of inquiry or made no commitments to do so -- even as Democrats say determining whether there was a financial link between Trump, his family, his business and Russians is essential to understanding whether there was any collusion in the 2016 elections.

Republicans have resisted calls to issue subpoenas for bank records, seeking Trump's tax returns or sending letters to witnesses to determine whether there were any Trump financial links to Russian actors -- calling the push nothing more than a Democratic fishing expedition.

While the top Democrat on the Senate Intelligence Committee has acknowledged that his panel lacks the resources of special counsel Robert Mueller to dig deeply into financial matters, several Democrats on committees with financial experts on their staff have sought such records. In the House Intelligence Committee, for instance, Democrats have asked for subpoenas to Deutsche Bank, the institution that has been a major lender to the Trump Organization as well as Jared Kushner, Trump's son-in-law and senior adviser.

"I think the allegations on money laundering are credible enough that we ought to, in the exercise of due diligence, see if this was one of the other vectors of the Russian active measures campaign," California Rep. Adam Schiff, the top Democrat on the House Intelligence panel, said earlier this month. "To me, that is far more potentially compromising than any salacious video would be."

Republicans have rebuffed them, arguing that falls outside the scope of the committee's probe.

"I don't see the link at this stage," Rep. Mike Conaway, the Texas Republican leading the House Russia investigation, told CNN. "Deutsche Bank is a German bank -- I don't see the nexus."

Asked about exploring Russian-Trump business transactions, Conaway was not moved. "I bet every big bank has a Russian customer somewhere," he said.

The partisan dispute over the Trump finances is a clear sign that Democrats plan to pursue these questions if they retake either chamber of Congress in this year's midterms. And it underscores how Republicans on the Hill have, for the most part, stayed away from vigorous oversight of the Trump administration -- something that is common when either party controls both Congress and the White House.

'Isn't that what Bob Mueller is doing?'

Some Democrats have concluded that Mueller's probe is their best hope for getting to the bottom of the Russian collusion question, though Trump himself has warned Mueller from crossing a red line into his family's finances.

House Oversight and Government Reform Chairman Trey Gowdy, who is also a top Republican on the House Intelligence Committee, has yet to issue a subpoena as chairman since he took the oversight gavel last June. The South Carolina Republican also brushed off calls by Democrats to pursue the money trail as part of the Russia investigation.

"Isn't that what Bob Mueller is doing?" Gowdy told CNN when asked about the matter.

On the House Financial Services Committee, the panel's ranking Democrat, Maxine Waters of California, for nearly a year has called on the committee's chairman, Jeb Hensarling of Texas, to issue subpoenas to Deutsche Bank and help pressure the Treasury Department to cough up documents from its Financial Crimes Enforcement Network (FinCEN) over any of Trump's past financial dealings.

Hensarling has resisted, citing investigations in other House committees, saying doing another one in his panel would be "redundant." And Deutsche Bank has ignored Waters' letters asking for a range of Trump-related information, suggesting it would not disclose confidential information, particularly without a subpoena.

Hensarling spokeswoman Sarah Flaim pointed to the inquiries that are ongoing in the House and Senate intelligence panels and by Mueller.

"Those investigations should be allowed to go forward," Flaim said. Hensarling's committee, she said, "will certainly review whatever information the investigations produce."

Foreign transactions

In addition to the calls for subpoenaing Deutsche Bank, Democrats point to the comments from Fusion GPS co-founder Glenn Simpson, who told the House Intelligence Committee last year that it should probe Trump's real estate deals in Florida and New Jersey, as well as Kushner's real estate dealings in New Jersey.

Democrats have also raised an interest in foreign transactions in places that include the Cayman Islands and Cyprus, particularly surrounding former Trump campaign chairman Paul Manafort. In April 2017, Rep. Mike Quigley of Illinois traveled to Cyprus to investigate how Russians used money laundering, a trip that came following an Associated Press report that Treasury officials obtained information regarding financial payments Manafort may have received through Cypriot banks.

Mueller's latest charges against Manafort and his former deputy Rick Gates on Thursday accused them of laundering $30 million and fraudulently securing more than $20 million in loans through real estate holdings. Some of the allegations occurred while Manafort and Gates worked on the Trump campaign, according to the indictment, although none of the activities were tied to their work on the campaign.

But those areas have gone largely unpursued on Capitol Hill.

Sen. Ron Wyden, ranking Democrat on the Senate Finance Committee and senior member of the Senate Intelligence Committee, has for months been frustrated with the lack of access to Treasury FinCEN documents. The Oregon Democrat recently fired off a letter for more Treasury documents, this time to obtain records about a lucrative 2008 real estate deal between Trump and a Russian billionaire that raised questions among Democrats about potential money laundering and suspect business dealings.

But Utah Sen. Orrin Hatch, the chairman of the Senate Finance Committee, has declined to join Wyden in these efforts. And he has rejected Wyden's requested to review Trump's tax returns in a private session.

"We're not going to do that," Hatch said in the Capitol. "He doesn't want to give up his tax returns, and I believe he's right."

'A policy dispute'

In an interview, Wyden said the Senate Intelligence Committee, under the chairmanship of Sen. Richard Burr, has shown little willingness to pursue these lines of inquiry as well.

"This is a policy dispute," said Wyden, who also sits on the Intelligence Committee. "The chairman does not believe that this is really the focus of the committee's work. I, on the other hand, say counterintelligence is right at the heart of our obligations. Counterintelligence 101 is following the money, because following money is how you compromise people."

Burr, a North Carolina Republican, pushed back at Wyden's assertions that the committee wasn't "following the money," but he declined to provide any details.

"Nothing has precluded him from digging further than what we've dug," Burr said of Wyden. "We've had access to whatever financial records we asked for."

Asked if that meant the panel has asked for Trump financial records, Burr said: "I'm not going to get into everything we've asked for. The investigation has explored all the areas we thought were pertinent."

Last year, Burr and the committee's ranking Democrat, Sen. Mark Warner of Virginia, did obtain some FinCEN documents amid threats to hold up a Treasury nominee. In an interview last month, Warner suggested that their panel didn't have the resources compared to the special counsel to dig through financial matters, saying Mueller has "tools we don't have" on financial issues.

The Senate Judiciary Committee has also investigated Russia's role in the 2016 elections -- and any ties with Trump associates. But the GOP chairman of the committee, Chuck Grassley of Iowa, made clear that investigating finances would not be part of the inquiry.

"That's not part of what we're doing," Grassley said.