Trump for America, Incorporated - an organisation established for the president's transition to the White House - claimed over the weekend that Special Counsel Robert Mueller's team had obtained tens of thousands of e-mails from the organisation unlawfully.

In a letter seen by Reuters, a lawyer for the still-existing transition group says investigators did not directly request the materials and instead obtained them from a separate federal agency called the General Services Administration, which stored the group's e-mails.

The special counsel's office waved off the transition team's complaint. A spokesman said "When we have obtained e-mails in the course of our ongoing criminal investigation, we have secured either the account owner's consent or appropriate criminal process."

Democrats say there is a wide-ranging effort by the president's allies on Capitol Hill and in some media outlets to discredit Mueller's investigation.

Some Republicans have argued that Mueller is biased against Trump and should be fired.

Whether or not it holds any weight, the Trump team's accusation adds to the growing friction between the president's supporters and Mueller's office as it investigates whether Russia interfered in the 2016 election and if Trump or anyone on his team colluded with Moscow.

President Donald Trump, when asked on Sunday if he was considering firing Mueller, told reporters, "No. I'm not."