Robinson, whose real name is Stephen Yaxley-Lennon, wrote on Saturday: "Over 800,000 (fake) Muslim refugees arrived in Germany in 2015,abt 100,000 in August alone. Germanistan not far off."
Nick Lowles, of the anti-fascist group Hope Not Hate, said it was good Robinson was "showing some compassion".
@TRobinsonNewEra good to see you are showing some compassion— Nick Lowles (@lowles_nick) September 5, 2015
@lowles_nick I'm happy to give asylum to any Sikhs , Hindus , Christians etc. we have millions of un integrated Muslims already— Tommy Robinson (@TRobinsonNewEra) September 5, 2015
Robinson famously quit the English Defence League nearly two years ago, after renouncing the movement's extremism and vowing to counter extremism.
He said at the time: "I thought the EDL was part of the solution but now it is part of the problem," adding: "I don’t hate Muslims... I don’t want to lead a revolution against Muslims."
"I acknowledge the dangers of far-right extremism and the ongoing need to counter Islamist ideology not with violence but with better, democratic ideas."
On Saturday the former leader also questioned why no other Islamic states have taken in any people fleeing Syria.
Over 57 Islamic nations and not even 1 is willing to accept these refugees instead they call for the 28 member state EU to accept them. Why?— Tommy Robinson (@TRobinsonNewEra) September 5, 2015
Robinson's comments come as people around Britain, moved by the picture of Aylan Kurdi, the three-year-old Syrian who drowned off a Turkish beach, have raised thousands of pounds for people in camps around Europe.
On Saturday people across the UK arranged to take vital supplies of food, clothing and shelter to thousands of people affected by conflict in the Middle East and Africa.
Small independent groups have also taken it on themselves to gather supplies to take across to France.
One group who set out to raise just enough money to deliver small donations of food and clothes to those living in migrant camps at Calais have already raised well over £110k.