The long-serving conservative who frequently criticised Mr Obama's foreign policy said Mr Trump's penchant for inflammatory tweets sent a message that "America doesn’t want to lead".
The world was "not sure of American leadership, whether it be in Siberia or whether it be in Antarctica," he told The Guardian.
Mr McCain, who ran unsuccessfully against Mr Obama for the Presidency in 2008, added: "As far as American leadership is concerned," the US' global standing had worsened under Mr Trump.
His comments came after the US President took to Twitter, to accuse Qatar, a key US partner in the Middle East and host to thousands of American troops, of "funding extremism".
He called a diplomatic blockade by the Gulf country's neighbours: "The beginning of the end to the horror of terrorism".
The social media posts put him at odds with his own Secretary of State, Rex Tillerson, who had called for a deescalation of the crisis.
Taking a quote from Mr Khan which people not to be alarmed by the presence of armed police, out of context, he wrote: "At least 7 dead and 48 wounded in terror attack and Mayor of London says there is 'no reason to be alarmed!' Pathetic excuse by London Mayor Sadiq Khan who had to think fast on his 'no reason to be alarmed' statement. MSM is working hard to sell it!"
Mr Trump's decision to withdraw the US from the Paris climate accord had also dismayed leaders around the world.
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