WASHINGTON—Secretary of State Rex Tillerson said Friday that a wave of arrests among the elite in Saudi Arabia raises “a few concerns,” as he is awaiting word on “how these particular individuals are dealt with.”

His assessment of the Saudi corruption investigation contrasted with comments from President Donald Trump, who on Monday said he had “great confidence in King Salman and the Crown Prince of Saudi Arabia, they know exactly what they are doing.”

Mr. Trump, writing on Twitter, added that “some of those they are harshly treating have been ‘milking’ their country for years!”

The mass arrests that have shook the Saudi elite come five months after Mohammad bin Salman was elevated to crown prince, and his government has been consolidating its grip on power. More than 200 people have been detained, mainly on corruption charges, including members of the royal family and cabinet officials.

Mr. Tillerson said many of those under arrest are “business and previous government ministerial people who the external world knows well.”