Mr Blair spent most of Friday attacking the PM over her hard line approach to Brexit negotiations and has been scathing about populist politicians like Mr Trump.
But he took a very different line when asked about Mrs May’s attempts to woo the controversial 45th President of the United States, during an interview with Bloomberg TV.
A decision to offer Mr Trump a state visit was met with an outcry of protest from politicians and the general public.
“Whether he enters Westminster Hall or not or addresses the Houses of Parliament, that’s a matter for Parliament and I won’t comment on it,” Mr Blair said.
Tony Blair backed the PM's attempts to charm President Trump
I certainly am not criticising the Prime Minister for reaching out to President Trump
“But of course he will come here [and] look whatever the situation is the British – American relationship is important.
“I certainly am not criticising the Prime Minister for reaching out to President Trump. It’s important that she builds a strong relationship.”
“Frankly right now I’ve got enough on my hands without entering into your political debate,” Blair concluded.
The former Labour PM gave a speech at Bloomberg in London on Friday and set out what he believes is a path to push for Britain to remain in the EU.
Blair slated the PM's approach on Brexit but approved of her approach to the US
He told the audience in central London: “What was unfortunately only dim in our sight before the referendum is now in plain sight.The road we're going down is not simply ‘hard Brexit’. It is Brexit at any cost.
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“Our challenge is to expose relentlessly what this cost is, to show how the decision was based on imperfect knowledge which will now become informed knowledge.”
Mr Blair’s tenure was characterised by a strong focus on the trans-Atlantic special relationship between the UK and the US.
This culminated in the joint invasion of Iraq in 2003 where he pledged full British support to President George W. Bush