In his speech, Trump said he was not there to "lecture" Muslim countries, but he did call for nations to promote "the aspirations and dreams of all citizens who seek a better life -- including women, children and followers of all faiths."
Secretary of State Rex Tillerson said on "Fox News Sunday" that the primary purpose of the visit was to confront the threat of terrorism, and that human rights would improve as security and stability in the region did.
"The way you address those human rights issues and women's rights issues is to improve the conditions in the region," Tillerson said. "There are efforts underway to, I think, improve the rights of women, the participation of women in society throughout the region."
Rep. Adam Schiff, a California Democrat, said on CNN's "State of the Union" that Trump had the "right message" on working with Muslim nations to fight terrorism, but decried what he saw as an attempt to "de-emphasize" human rights and the promotion of democracy abroad.
"I think that would be a terrible abdication of our global leadership when it comes to advocating for people who are the subject of persecution," Schiff said.
In an interview on the same program, Florida Sen. Marco Rubio, a Republican, said the "lecture" line certainly wouldn't have been in a speech of his, illustrating the gulf between his preferred approach and that of the White House.
"I'm much more forceful and open and vocal about criticizing, whether it's Egypt or Saudi Arabia for its human rights record," Rubio said. "The White House is convinced they can get better results by addressing those issues in private, one-on-one."
Arizona Sen. John McCain said on Fox that while the President's Saudi Arabia trip was going well, it needed to include a robust call for US values.
"We have to stand up for what we believe in," McCain said.
Many of the autocratic nations in the region, including Saudi Arabia, have severe restrictions on women's rights and participation in society. Under the Saudis' strict Wahhabi interpretation
of Islam, for example, women cannot drive, open bank accounts, work, travel or go to school without the express permission of a male guardian. In 2011, the country beheaded a woman
for "witchcraft and sorcery."
Saudi Arabia's poor track record on human rights forced the Obama administration to strike an awkward balance between condemning
its human rights abuses and maintaining its support in the fight against terrorism. In the final weeks of the previous administration, the US also halted some
arms sales to the kingdom over its killing of civilians in Yemen's civil war. Trump, however, inked an arms deal
with Saudi Arabia on Saturday worth over $100 billion, signaling a renewed commitment to the alliance.
Democratic and Republican presidents since Franklin Delano Roosevelt have looked past Saudi Arabia's treatment of its own people to build stronger ties with the royal family there even while calling for the spread of democracy and human rights around the world.