President Barack Obama pauses while addressing an audience during a campaign fundraising event, in Boston.
"We are very respectful of the sovereignty of Pakistan but we cannot allow someone who is actively planning to kill our people or our allies' people, we can't allow those kinds of active plans to come to fruition without us taking some action," he added.
Elite US commandos who were whisked into Pakistan by helicopter killed al Qaeda leader bin Laden on May 2. The secret operation ended the most elaborate manhunt in history.
The BBC interview was conducted last Thursday at the White House, ahead of Obama's European tour this week. The US president is due to visit Ireland, Britain, France and Poland.