RIYADH, Saudi Arabia — Secretary of State Mike Pompeo, speaking with unusual candor, said Sunday that the United States had tried but failed to end a Saudi Arabia-led blockade of Qatar, a crucial military partner in the Middle East.

He also said Saudi leaders needed to ensure that they would take full responsibility for the death last fall of Jamal Khashoggi, an outspoken dissident who lived in Virginia and who was killed on a visit to the Saudi consulate in Istanbul.

Mr. Pompeo made his remarks in Doha, Qatar, just before flying to Riyadh, the Saudi capital, where he is scheduled to meet with Crown Prince Mohammed bin Salman, the kingdom’s most powerful figure, on Monday.

Taken together, the comments underscored the challenges faced by the Trump administration as it tries to maintain its relationship with Saudi Arabia and build a coalition against Iran, while mitigating the fallout from a range of actions undertaken by the kingdom and Prince Mohammed, its de facto day-to-day ruler.