John Dowd, Trump's personal lawyer, praised Sessions on Saturday for firing McCabe, and then suggested that Deputy Attorney General Rod Rosenstein, who oversees the special counsel, "bring an end" to Mueller's investigation.
Stephanopoulos also asked about this week's announcement by the Republican majority on the House Intelligence Committee that they are ending their probe of Russia's meddling in the 2016 election after concluding there was no collusion by the Trump campaign.
Trump, a Republican, has renewed his Twitter attacks on both the Federal Bureau of Investigation and Mueller's probe since the firing on Friday of the bureau's former deputy director, Andrew McCabe, days before he was eligible to retire with a full pension.
Schumer calls on Republicans to back Mueller
Marco Rubio said McCabe should have been allowed to retire-he was sacked less than 48 hours before he was due to retire. Trump, meanwhile, posted a series of tweets on McCabe, Comey, and Mueller Saturday evening and Sunday morning.
McCabe said in a statement late Friday that Trump had him removed as part of an effort to undermine federal law enforcement in general and the Russian Federation investigation in particular.
In a tweet Sunday, Michael Bromwich says McCabe won't be responding to Trump's "childish, defamatory, disgusting & false" tweets. "But the tweets confirm that he has corrupted the entire process that led to Mr. McCabe's termination and has rendered it illegitimate". The President's own Attorney General Jeff Sessions put Rosenstein in charge of Mueller's investigation. Fueling Mr. Trump's aggravation now is the special counsel's latest inquiry: a subpoena to the Trump Organization.
House Speaker Paul Ryan, R-Wisconsin, issued a statement regarding Mr. Trump and his harsh words for Mueller to the New York Times.
McCabe, in a statement after his firing, called his ouster "retribution", saying, "I am being singled out and treated this way because of the role I played, the actions I took, and the events I witnessed in the aftermath of the firing of [former FBI Director] James Comey".
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Republicans strongly cautioned the President and his team to let Mueller do his work. Another Dem recently added ... does anyone think this is fair?
Republican allies of the president have seized upon the fact that some of Mueller's team - seven out of 17 lawyers, according to The Washington Post - previously donated money to Democratic political candidates. That report is expected to conclude McCabe was not forthcoming about matters related to the FBI investigation of Democrat Hillary Clinton's emails.
But Mr Mueller defenders say he, and more broadly the FBI, have safeguards in place to avoid letting any investigation be tainted by politics. "And I think the reality, Margaret, is that yes, there's a growing frustration that after more than a year and millions and millions of dollars spent on this, there remains no evidence of collusion with Russian Federation". "We can't in Congress accept that", Flake told CNN's "State of the Union". Graham repeated a previous comment that removing Mueller would be the beginning of the end of Trump's presidency.
The Republican senator and frequent Trump critic Jeff Flake likewise warned on CNN that ousting Mueller was seen as "a massive red line that can't be crossed".
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Rep. Trey Gowdy, R-S.C., a member of the House Intelligence Committee, warned Trump that any interference in the Mueller probe would result in "a very, very long, bad 2018".