US Senate Democrats have urged the Senate Finance Committee to review President Donald Trump's tax returns, as part of a campaign in Congress that has begun to show signs of attracting Republican support.

Defying decades of precedent, Trump has refused to release his tax returns while his tax affairs are under federal audit. Democrats and other critics contend that the documents could show whether his global business empire poses any conflicts of interest as the president moves his agenda forward on issues ranging from tax reform to foreign relations.

In a letter dated Wednesday, seven Democrats on the Senate Finance Committee urged the panel's Republican chairman, Orrin Hatch, to request the documents from the US Treasury so that lawmakers can review them in a closed session and determine whether the returns can be released to the public.

Democrats in the House of Representatives said they planned to pose a similar request on Thursday to Hatch and House Ways and Means Committee Chairman Kevin Brady in a bipartisan letter signed by 140 lawmakers, including House Republicans Mark Sanford of South Carolina and Walter Jones of North Carolina.

The Democratic efforts face long odds in the Republican-controlled Congress. Three attempts in the House have met with defeat this year.

Hatch and Brady responded to the Senate request in a joint letter saying Democrats were suggesting "an abuse of the tax-writing committees' statutory authority" that would set "a dangerous precedent".

Democrats say they hope to create a bipartisan juggernaut to require the disclosure of Trump's and future presidents' tax returns by pushing forward on multiple fronts.

On Monday, the House voted down a Democratic effort seeking the Republican president's returns, with Sanford and Jones voting "present" rather than opposing the measure.

Republican Senator Susan Collins of Maine told an interviewer last month she could be open to a subpoena of Trump's taxes as part of a Senate Intelligence Committee probe of alleged Russian meddling in the 2016 presidential elections.

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On Wednesday, Politico quoted Republican Senator Lindsey Graham of South Carolina as saying he wanted presidential candidates to be required by law to release their tax returns beginning in 2020.

"The tax return is the lowest ethical bar that you can have for a presidential nominee or a president," said Senator Ron Wyden of Oregon, top Senate Finance Democrat who introduced legislation in January requiring nominees and sitting presidents to disclose their returns.