The prime minister also urged fellow EU leaders to step back from harsh tit-for-tat reprisals – planned for next month – against the US, calling for their response to be “proportionate”.
No bilateral meeting with Mr Trump is scheduled for the two day summit in Canada, with the US president arriving late and expected to leave early.
He described the gathering of the Western economic powers as a “distraction” – ahead of his summit with North Korea next week – despite the growing fears of a disastrous global trade war.
However, speaking to reporters before landing in Quebec, Ms May insisted Mr Trump did make a positive contribution at international summits, pointing to his willingness to tackle online terrorist propaganda.
She urged critics to “look at President Trump at the last G7”, adding: “Crucially, one of the issues we agreed on was taking down terrorist material online from the internet.
“It was important that America was sitting around that table and agreed that with us. We have been able to take action with companies in America as a result.”
Ms May added: “What we are seeing with President Trump is what we hope is a very positive step forward in relation to North Korea.”
The two day meeting will be dominated by the possibility of a trade war – prompted by the US levies of 25 per cent on steel and 10 per cent on aluminium.
Angela Merkel, the German chancellor, has predicted a big fight at the summit, triggering suggestions it has become a “G6+1” – with the US president isolated and alone.
The EU is poised to impose tariffs on US imports ranging from Harley-Davidson motorbikes and jeans to bourbon, peanut butter, cranberries and orange juice, from next month.
Brussels is still finalising the list it will submit to the World Trade Organisation (WTO), which will be on top of tit-for-tat tariffs on about £2.5bn of US steel.
In the interview, the prime minister repeated her criticism – made in a phone call to Mr Trump this week – that the US tariffs were “unjustified”.
But she added: “Obviously, the EU will be responding. We want to ensure we are working with others in the European Union to ensure that response is proportionate, that it is within the WTO rules.
“We want to be a great champion for free trade around the world, and that’s what we will continue to be.”
No 10 sources denied that Mr Trump had refused a bilateral meeting with the prime minister, suggesting it had been clear early on that he would attend no one-to-ones.
However, such a meeting would have been highly prized, if available – and Ms May will meet individually with Ms Merkel, Emmanuel Macron and other leaders over the next few days.
Asked if she was too “politically correct” – a charge Mr Trump has made of other, unnamed leaders – she replied: “I just get on and make sure I’m delivering and delivering what people want. That’s the job of any politician.”
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies