U.S. intelligence indicates Iran was the staging ground for a debilitating attack on Saudi Arabia’s oil industry, people familiar with the matter said, as Washington and the kingdom weighed how to respond and oil prices soared.

Monday’s assessment, which the U.S. hasn’t shared publicly, came as President Trump said he hoped to avoid a war with Iran and as Saudi Arabia asked United Nations experts to help determine who was responsible for the airstrikes.

The...