Mueller is looking into the alleged Russian interference in the 2016 US presidential election and any potential collusion between the Trump campaign and Moscow, among other matters that may arise from the investigation.
In a reference to the special prosecutor who is heading-up the Russian Federation probe, the president added: "Bob Mueller is totally conflicted, and his 17 Angry Democracts that are doing his dirty work are a disgrace to the United States of America!".
The joint appearance by Coats, Secretary of Homeland Security Kirstjen Nielsen, national security adviser John Bolton, FBI Director Christopher Wray and National Security Agency Director Paul Nakasone comes as the administration is facing criticism over its efforts to deal with election interference and continuing questions over how seriously President Donald Trump takes the threat. "The President has expressed the same opinion".
Trump attorneys say both sides have exchanged proposals for conditions for such a Trump interview.
Trump has repeatedly termed the probe as "a hoax".
Giuliani also told reporters the president's legal team was in the middle of ongoing negotiations with Mueller, as a report in The Washington Post said the special counsel had offered to reduce the number of questions in exchange for a sit-down interview.
Trump's legal team is said to be preparing a response to send to Mueller within the next three days, per the Times.
Senator Dianne Feinstein, the top Democrat on the Judiciary Committee, said after Trump's tweet, "It's clear to me he's very anxious about it and he wants to prevent it any way he can".
"Sky News' US correspondent Mark Austin said: "(Mr Trump) is consistently trying to undermine his attorney general and the Mueller investigation. While the White House has said the president's tweets amount to official statements, the president's personal attorney Rudy Giuliani later Wednesday issued a statement to ABC News describing the tweet merely as Trump's "opinion".
Trump critics said they read the tweet as pointed interference in the Mueller investigation. First, we know this because the USA intelligence community unanimously concluded that Russian Federation intervened in the 2016 election in order to help Trump win.
"Just because @realDonaldTrump obstructs justice in full public view by calling on Sessions to interfere in Mueller investigation doesn't mean it's not obstruction of justice".
"I don't know why Rudy seemed to think that obstruction by tweet is a insane notion", Rodgers said.
"The only person who could fire Mueller is Rod Rosenstein, who is bound by Justice Department guidances that specify that he would have to have good cause, and it would have to be reported to Congress", Collins said. They've still come up with nothing in regards to the president.
For months now it seems Trump has been declaring "there's no collusion" in reference to the possible ties between Russian Federation and the Trump 2016 presidential campaign. "We have every reason to believe they don't have anything of the president doing anything wrong".