LONDON — Wearing a green hat and coat, Queen Elizabeth II on Tuesday became the first British monarch in a century to set foot on Irish soil, during a trip designed to celebrate improved Anglo-Irish relations.

In a scene that seemed impossible until recently, the British anthem, “God Save the Queen,” rang out moments before the queen laid a wreath at a garden in Dublin dedicated to those who lost their lives struggling for Irish freedom, often against oppressive British control.

But the historic nature of the tour threatened to be overshadowed by security jitters.

After a telephone tip, an improvised explosive device was discovered on a bus outside Dublin late Monday, just hours before the queen arrived in Ireland with her husband, Prince Philip. The bomb, described as “viable” by Irish police, was disabled....