After severing ties with Qatar on Monday, Saudi Arabia said it was committed to "decisive and swift action to cut off all funding sources for terrorism" in a statement carried by state news agency SPA, attributed to "an official source".
And in a separate statement issued on Friday, the United Arab Emirates praised Trump's "leadership in challenging Qatar's troubling support for extremism".
Trump accused Qatar of being a "high level" funder of terrorism on Friday, even as the Pentagon and US Secretary of State Rex Tillerson cautioned against the military, commercial and humanitarian effects of a blockade imposed by Arab states and others.
A separate SPA report on Saturday acknowledged Tillerson's call for Qatar to curtail support for terrorism, but did not mention his remarks that the crisis was hurting ordinary Qataris, impairing business dealings and harming the US fight against the Daesh (also known as ISIL or ISIS) militant group.
Saudi Arabia said its action followed the conclusions of last month's Arab Islamic American Summit in Riyadh, where Trump delivered a speech about Islamic extremism.
Trump said he helped plan the move against Qatar, although a senior administration official told Reuters earlier this week that the US had no indication from the Saudis or Emiratis during the visit that they would sever ties with Qatar.