Hundreds of protestor gather outside Donald Trump's luxury golf resort and have spread across the rest of Scotland.
It said it had informed police about the stunt 10 minutes before the glider arrived.
We are investigating a breach of the air exclusion zone over Turnberry hotel, which is a criminal offence.
Trump is set to depart Scotland on Sunday (July 15) for a meeting with the Russian leader Vladimir Putin in Helsinki, Finland.
Eli Roth, 56, from California but living in Edinburgh, said he doubts the USA president will take notice. It is 6.5m tall and was bought with crowd-funding Image caption There was even a Trump coconut shy at the protest Image caption Armed police were at Carnival of Resistance in The Meadows Image caption Froydis Fossli Moe, said: 'I came here to show my support to the leftist part of society.
She said the turnout for the events in Edinburgh had "surpassed all expectations, adding: "We reckon over 60,000 people have taken part in what's been happening, come to the Parliament for the start, been on the march, been here at this wonderful Carnival of Resistance".
Wearing a white baseball cap with United States of America stitched on it, the president waved to the protesters, who stood behind a row of police officers on the outskirts of the luxury golf resort.
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In a joint statement, Leonard and Harvie said: "For Donald Trump to travel to Scotland with public assistance and ease when his travel ban has caused outrage and despair around the world would simply not be acceptable".
"But personally, I don't think we should have been rolling out the red carpet for Donald Trump".
Graham Creelman, 70, a retired journalist with ITV and BBC, who also spoke to The Scotsman at the protests, said: "I don't disagree with the right of the American people to elect him".
The president has since told media that he didn't criticise Ms May, calling the claim "fake news".
He and the first lady also met the Queen for tea at Windsor.
Trump's visit to Scotland follows a two-day working trip to England, and meetings with British Prime Minister Theresa May and Queen Elizabeth, during which an estimated tens of thousands of protesters marched in London.
Trump directly criticised Prime Minister Theresa May's Brexit strategy, saying it had probably killed off hope of a U.S.
May was looking forward to sitting down with Trump to talk him through the negotiating stance at Chequers, her spokesman said when asked about the Trump comments.