WASHINGTON — A White House radar system designed to detect flying objects like planes, missiles and large drones failed to pick up a small drone that crashed into a tree on the South Lawn early Monday morning, according to law enforcement officials. The crash raised questions about whether the Secret Service could bring down a similar object if it endangered President Obama.

The drone, which was about two feet in diameter and weighed about two pounds, was operated by a government employee whom the Secret Service did not identify. The agency said the employee was flying the object near the White House around 3 a.m. for recreational purposes when he lost control of it. Officials did not explain why the man, who does not work at the White House and who has not been charged with a crime, was flying the drone at that hour.

The crash was the latest security breach showing the difficulties the Secret Service has had protecting the White House in recent years. In September, a man with a knife climbed over the White House fence and made it deep inside the building before officers tackled him. In 2011, a gunman fired shots that hit the White House while one of the Obama daughters was home.

On Monday, a Secret Service officer who was posted on the south grounds of the White House “heard and observed” the drone, the agency said, but the officer and others stationed at the residence were unable to bring it down before it passed over the White House fence and struck a tree. The drone was too small and flying too low to be detected by radar, officials said, adding that because of its size, it could easily have been confused for a large bird.