"I'd like to begin by sending our thoughts and prayers to the people of Puerto Rico, who have been struck by storms of historic and catastrophic severity", Trump said.
The president opened his speech on tax reform with his comments on the federal government's relief efforts in Puerto Rico.
Cruz on Friday also bristled at suggestions that the relief effort had been well-coordinated.
"This is a story of a devastation that continues to worsen because people are not getting food and water", Cruz said on CNN. "What you see here with me is not the reality of the people of Puerto Rico".
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Having a commander who reports both to the governor and the military chain of command will create a "unified team" of military and civilian disaster response units, Craig Fugate, the head of the Federal Emergency Management Administration during the Obama administration, said in a phone interview.
The White House said Trump will make calls to several Puerto Rico officials, including Gov. Ricardo Rosselló, on Saturday afternoon.
San Juan's Mayor Carmen Yulin Cruz, left, hugs a woman during her visit to a nursing home in San Juan, Puerto Rico on September 22. After much pressure, the White House also announced a 10-day waiver of the Jones Act, lifting the shipping restrictions into us ports, and thus allowing food and supplies to be brought into Puerto Rico.
In another tweet, he blamed "Fake News CNN and NBC" for going out of their way "to disparage our great First responders".
Cruz's comments on Friday were in response to a senior US official calling the disaster response in Puerto Rico "a good news story". I have no time for distractions. "This is a people are dying story. This is a life-or-death story". The Caribbean island has been without power for a week and is suffering shortages of reliable drinking water.