Special counsel Robert Mueller has reportedly obtained tens of thousands of emails from US President Donald Trump's transition team as part of a probe into the 2016 election.
So far the FBI has charged four people as part of the investigation.
A lawyer from the Trump for America group has alleged the emails were obtained unlawfully from a third party.
A letter he sent to US lawmakers alleges their constitutional rights may have been breached by the disclosure.
The group had been using a government agency, the General Services Administration (GSA), for their offices, equipment and email hosting in the period between Donald Trump's election and his inauguration in 2017.
The GSA is reported to have supplied these records to Mueller's investigation team in the summer.
Kory Langhofer, a lawyer for Trump for America, sent a letter to Congress on Saturday complaining that the GSA "did not own or control the records in question".
The letter says the group believe some of these communications should have been redacted because they believe they contain information under privilege. The seven-page letter was published by political news website Politico.
Mr Langhofer said Trump for America had separated those emails out in advance of any request to share them, but found out on Tuesday and Wednesday that Mr Mueller's probe had already obtained the emails months ago.
The transition group lawyer is requesting that Congress act to protect future presidential transitions from having "private records misappropriated by government agencies, particularly in the context of sensitive investigations intersecting with political motives".
Others have hit out at claims the emails were obtained unlawfully. Renato Mariotti, a former federal prosecutor, said the move was not inappropriate or not even unusual in a widely-shared tweet.
Democratic Representative Eric Saldwell tweeted that the claims were "another attempt to discredit Mueller as his #TrumpRussia probe tightens".
American news website Axios reported on Saturday that email records from 12 members of the campaign, including President Trump's son-in-law Jared Kushner, had been obtained by the Mueller team.
Reports in US media suggest President Trump's private lawyers are expected to meet Mr Mueller and members of his team next week to discuss the next phases of the investigation.
Earlier this month the president's former national security advisor Michael Flynn became the highest-profile person charged in the probe, pleading guilty to making false statements to the FBI about meetings with Russia's ambassador weeks before Donald Trump's inauguration.
It was revealed he is co-operating with the inquiry's investigation.