"Hacking by foreign entities or anyone in the American campaign is assisting is a crime", he continued.
Both approaches were rubbished by Giuliani on Monday.
Speaking to CNN "New Day" co-host Alisyn Camerota, Giuliani first downplayed the president's relationship with his embroiled former campaign chairman, Paul Manafort, who faces charges resulting from the Mueller probe.
Giuliani made headlines Monday when he gave a series of rambling TV interviews in which he stated that "collusion is not a crime".
Mr Trump's tweet comes after his lawyer Rudy Giuliani told Fox News "collusion is not a crime".
The question of whether President Trump obstructed justice in the FBI's investigation of Michael Flynn has always hinged on his familiarity with the details of that probe - and when he learned them.
Specifically, the memo states that allegations Manafort "committed a crime or crimes by colluding with Russian government officials with respect to the Russian government's efforts to interfere with the 2016 election" are "within the scope" of the special counsel's investigation.
Special counsel Robert Mueller is investigating possible cooperation between Trump's presidential campaign and Russians who sought to influence the 2016 United States election by hacking into Democratic computers and using social media to try to undermine Democrat Hillary Clinton. "The president didn't hack", Giuliani said on CNN. Trump wrote on Twitter.
Cordero went on to add that criminal violations could, however, emerge if there was evidence of hacking or a violation of campaign finance laws related to Mueller's investigation.
The Trump team began publicly arguing this assertion since late past year.
He said Trump will not agree to a sit-down with Mueller until certain parameters are set.
Giuliani also said Mueller has "conflicts of interest". "But there's no violation of law, statute, rule or regulation that we have seen after reviewing this case for a year, and I think Bob Mueller will come to the same conclusion".