Saudi Arabia, which has deep, long-standing energy and defense ties to the United States, was not named in the travel bans.
During Trump's three days in the Middle East kingdom, a weapons deal worth more than $100 billion is set to be unveiled, and the Saudi royals have invited dozens of leaders from across the Muslim world to meet Trump.
Building an alliance
The president, confronted by growing political scandals at home, intends to use the visit to portray his administration as a global leader by helping birth an alliance with like-minded Muslim leaders to combat "radical Islamic terrorism" (Trump's phrase and one the Saudis do not want to use).
"It lays to rest the notion that America is anti-Muslim," Saudi Foreign Minister Adel al-Jubair told reporters earlier this month.
"It's very important that the president is reaching out to Muslim-majority countries in the world, and trying to identify who our friends are and work with them to beat our common enemies," Democratic Congressman Thomas Suozzi, a member of the House Foreign Affairs Subcommittee on the Middle East told VOA. "We have to recognize that most of the Muslims in the world are peace-loving people, who have strong faith and want to have a harmonious world we need to embrace."
A shared vision, with the Gulf Cooperation Council and Organization of Islamic Cooperation, to enhance the battle against the so-called Islamic State group and al-Qaida, also would be interpreted as putting President Trump squarely on one side of the Sunni-Shi'ite ideological schism in the Muslim world.
The Saudis are Sunnis (Islam's majority), while Iran is dominated by Shias.
U.S. President Donald Trump';s and Saudi Arabia';s King';s Salman bin Abdulaziz Al Saud';s photos are seen with flags of both countries on airport road as part of celebrations to welcome United States President Donald Trump, in Riyadh, Saudi Arabia, May 19, 2
'Big symbolic gesture'
Saudi Arabia and Iran support rival proxy forces in conflicts throughout the region, including in the two significant civil wars in Yemen and in Syria, where the embattled forces of President Bashar al-Assad are backed by Tehran and Moscow.
"Going to Riyadh is a big symbolic gesture to Iran," Hudson Institute adjunct fellow Mike Pregent told VOA.
The Middle East analyst adds that the attempt to forge new alliances among anti-Iran regional powers is occurring because "the biggest threat they see after ISIS (Islamic State) is Iran and ISIS never goes away because of Iran."
While administration officials say Trump is a strong believer in human rights, they acknowledge this will not be a significant topic of discussion here.
That angers some.
"If countering violent extremism is a priority for this administration and it wants to defang this ideology, then Saudi Arabia is a very odd partner for that project," Human Rights Watch Middle East Executive Director Leah Whitson told VOA. "The Saudi government and its policies are among the biggest sources of violent extremism."
Toby Keith performs at the 'Make America Great Again! Welcome Celebration' concert at the Lincoln Memorial in Washington, Jan. 19, 2017.
Toby Keith to perform
During the president's stay, American country music singer Toby Keith, who performed at Trump's January inauguration, will hold a free concert here for men only.
A country where women are not allowed to drive automobiles and has mandatory sex segregation represents "intolerance and extremism that the United States should not stand behind," said Whitson.
To demonstrate their earnestness for an even closer alliance with Washington, the Saudis also are hosting a social media forum where Trump is to deliver a speech Sunday to the Muslim world. In addition, the Saudis are organizing a counterterrorism conference, opening a center to "fight radical thought" and predicting that some significant business deals will be signed at a forum for chief executives.
(VOA Russian Service reporter Natasha Mozgovaya contributed to this report.)