Earlier, The New York Times published a confidential 20-page letter the American president's legal team sent to Mueller in January, along with another sent in June 2017.
Trump's brash assertion of presidential power...contends that the president can not illegally obstruct any aspect of the investigation into Russia's election meddling because the Constitution empowers him to, "if he wished, terminate the inquiry, or even exercise his power to pardon".
The government price tag of US Special Counsel Robert Mueller's probe into Russia's alleged interference in the 2016 US presidential elections stood at about $16.7 million in its first 10 and a half months, according to the AP.
In a Saturday tweet, Trump asked whether the special counsel or Justice Department had leaked the letter to the media. Trump, for his part, has a couple of times lambasted Mueller's investigation, calling it "witch hunt".
The president on Saturday afternoon addressed the letter directly on Twitter.
Russian Federation has denied any interference and Trump has repeatedly said there was no collusion or obstruction of justice.
Though it is written as a defense of the president, the letter recalls the tangled drama of early 2017 as the new administration dealt with the Russian Federation investigation.
A memo dated January 29, 2018, argues that the Constitution gives the president vast authority to, for instance, fire FBI Director James Comey, and even argues that the president can not obstruct justice by terminating an investigation.
In a letter to Mueller, Trump's lawyers argued he could not obstruct justice.
In addition to reportedly pushing Sessions to reverse his recusal, both personally and through surrogates like White House counsel Don McGahn, Trump has also publicly attacked the attorney general amid his frustration, calling him "weak" and "beleaguered". It contends that Trump has the power to shut down any investigation by the FBI or Justice Department "at any time and for any reason".
"As all of the evidence demonstrates, every action that the president took was taken with full constitutional authority pursuant to Article II of the United States Constitution", Sekulow and Dowd wrote.
It also serves as a reminder that in weighing an obstruction case, Mueller is reviewing actions and conversations involving senior White House officials, including the president, the vice president, and the White House counsel.
In all, the letter presents a broad view of presidential authority - and one the Times says could be challenged in court if Mueller does issue a subpoena to Trump.