The measure, entitled the "Protection Of The Nation From Foreign Terrorist Entry Into The United States", has since Friday blocked travelers from the "terror-prone" countries of Syria, Yemen, Sudan, Somalia, Iran, Iraq, and Libya from entering U.S. soil for a period of 90 days.
The official Saudi Press Agency did not mention safe zones in its report on the call.
Saudi Arabia's King agreed to Trump's proposal to implement a safe zone in Syria in a Sunday phone call. The new USA president, however, stopped short of vowing to repeal the accord, saying he agreed with the Saudi king on "the importance of rigorously enforcing" it, according to the White House.
During their call on Sunday, Trump and King Salman also committed to "address Iran's destabilizing regional activities" and reaffirmed their commitment to the US-Saudi Arabia strategic alliance. The President voiced support for the Kingdom's Vision 2030 economic program.
"My number one priority is to dismantle the disastrous deal with Iran", Trump said at the conference in March 2016, calling the controversial agreement signed between the P5+1 world powers and Tehran "catastrophic for America, for Israel and for the whole of the Middle East".
Saudi Arabian Airlines (Saudia) has issued an advisory that it will not allow passengers holding Iraqi, Iranian, Syrian, Yemeni, Libyan, Sudanese and Somali passports to travel to the United States aboard its planes.
The White House stated that the two leaders discussed "the importance of strengthening joint efforts to fight the spread of radical Islamic terrorism", while the statement from the Saudi government instead referred generally to "terrorism". Bin Laden also wanted to use the attacks to expand and recruit for al-Qaeda in Saudi Arabia, the person said.
Egypt, Saudi Arabia and the United Arab Emirates have designated the Brotherhood a terrorist organization. Riyadh fears the Brotherhood, whose Sunni Islamist doctrines challenge the Saudi principle of dynastic rule, has tried to build support inside the kingdom since the Arab Spring revolutions.
According to Reuters, a debate is under way inside the Trump administration on whether the United States should also declare the Brotherhood a terrorist organization and subject it to usa sanctions.
King Salman also gave his support to the creation of safe zones in Yemen, where a Saudi-led Arab coalition is now bombing Houthi rebels at the request of the exiled Yemeni government.
In a separate phone call with Crown Prince Sheikh Mohammed bin Zayed, Mr Trump discussed "groups that raise fake slogans and ideologies [that] aim to hide their criminal truth by spreading chaos and destruction" - which is likely to be reference to the Muslim Brotherhood.