David Haines, 44, was beheaded in Syria three years ago by the group after being held prisoner for 18 months.
His elder brother Mike, who works with groups to combat extremist indoctrination of young people in the UK, said it was "vital" that communities "remain calm and united", regardless of the motive.
Police believe they know the identify of the as-yet unnamed suspect, who was killed following his rampage through central London which resulted in Pc Keith Palmer and three members of the public being killed.
Around 40 others were hurt, with some described as suffering "catastrophic" injuries.
Mike Haines said: "My thoughts and prayers go out to the family and friends of the victims of this tragic attack in the heart of our nation's capital.
"In the midst of the hurt and heartache that we are all feeling in this moment, it is vital that we as a society remain calm and united, no matter who or what was behind this attack.
"Terrorism, in all its guises, seeks to spread fear and divide us. In confronting this evil, we must stand shoulder to shoulder, with confidence that we are all stronger when we stand together.
"The reports of kindness and solidarity amongst those on the scene, proves our togetherness.
"Whatever the motivations, they will not succeed in sewing distrust amongst us - I have seen first hand that we are stronger than that."
Yorkshire-born David Haines, who was brought up in the Perth area of Scotland, was one of a string of hostages beheaded by IS, whose filmed executions involved the notorious Terrorist Jihadi John.
The former RAF engineer's name was eventually made public when he appeared in the background of a video showing the execution of Steven Sotloff, an American journalist also seized by terrorists.