Allegations Kushner's finances are being studied as part of the investigation come after it was reported last month the team behind the probe were examining meetings he had with Russian Ambassador Sergey Kislyak and a Russian banking executive late previous year during the presidential transition.
The US president's attack, which appears to target Rod Rosenstein, the deputy attorney general whois leading the government investigation, reflects Mr Trump's mounting frustration with the unrelenting controversy that has consumed his early presidency.
Mueller is expected to interview top intelligence officials to examine whether Trump tried to influence or push for a shut down of the Russian Federation investigation altogether - i.e., obstruct justice.
The White House has used a memo written by Mr Rosenstein to justify Mr Trump's decision to sack Mr Comey, but that Trump action may now be part of the probe.
Rosenstein has been overseeing the Russian Federation probe since shortly after Attorney General Jeff Sessions recused himself.
Following Comey's blockbuster appearance before Congress, an Associated Press-NORC Center for Public Affairs Research poll shows 68 per cent of Americans are at least moderately concerned about the possibility that Trump or his campaign associates had inappropriate ties to Russian Federation. The Washington Post reported this week that Mueller is investigating whether Trump attempted to obstruct justice when he suggested Comey drop an FBI investigation into Michael Flynn, Trump's former national security adviser, as well as when he fired Comey.
"After 7 months of investigations & committee hearings about my 'collusion with the Russians, ' nobody has been able to show any proof".
The interest in Kushner's activities by the special counsel's office is no more extensive than the FBI's interest in his multiple roles on both the Trump campaign and transition team, which CNN reported last month.
Though some in the White House have preached caution, fearing a repeat of the firestorm over Comey's firing, many in Trump's orbit - including his son Donald Trump Jr. and adviser Newt Gingrich - have deemed Mueller biased and worthy of dismissal.
A Justice Department spokesman declined to comment on the tweet.
"He is a man of extraordinary independence and integrity. and great character", Vice President Mike Pence told reporters on Wednesday, noting that the longtime Justice Department official "came to work, sat down and made his recommendation" to fire Comey.
The special counsel overseeing the probe into Russia's alleged meddling in the United States election is also looking at whether President Donald Trump tried to obstruct justice, media reports say, citing unnamed officials.
The tweet raised speculation that Rosenstein may also have to recuse himself from the probe if Mueller turns his attention to Trump's decision to fire Comey.
Today, in another series of furious tweets, it seems Trump has inadvertently confirmed this news.
Mr Pence hired criminal lawyer Richard Cullen as special counsel Robert Mueller's investigation intensifies. Comey testified that Trump's demand for "loyalty" came in the context of a conversation about whether Comey would continue to serve as Federal Bureau of Investigation director at his pleasure. Trump publicly admitted he fired Comey because of unhappiness with the Russian Federation investigation. "President Trump said prior that once he gets in he's going to kick the S-H-I-T out of the enemy".
Trump also retweeted law professor Alan Dershowitz, who has called for a halt to conversations about obstruction of justice because there was "no plausible case". He also has millions of followers on his official Facebook pages.
It was unclear what report or reports Rosenstein was referencing.