The trio met in Berlin where the Germany's Protestant Church Assembly is taking place.
Thousands have gathered for Kirchentag where a series of events are marking the 500th anniversary of the reformation.
Through faith, love, and resolve the character of the people of Manchester has shown itself. Our thoughts & prayers are with you. https://t.co/rZyZaQVWT2
— Barack Obama (@BarackObama) May 25, 2017
Addressing the people of Manchester, Mr Obama said: "As a father of two daughters I'm heartbroken by the extraordinary tragedy in Manchester.
"It's unimaginable to think about the cruelty and violence the city has suffered. Our thoughts and prayers are with all of you.
"What I want to emphasise is that through faith and resolve the character of Manchester has shown itself with kindness.
"The entire world is in solidarity with you."
Thank you @BarackObama and Chancellor #Merkel for sending these messages to the people of #Manchester when we met in Berlin today. pic.twitter.com/mSD2cuM92T
— Justin Welby Ù† (@JustinWelby) May 25, 2017
In a short video posted on Twitter, Justin Welby ended by echoing the words of the Bishop of Manchester when he said "love conquers hate".
President Obama will travel from Berlin to Edinburgh where tomorrow he will address philanthropy and business leaders.