He added that Democrats had inflated the official death toll to "make me look as bad as possible".
The Republican president suggested the hurricane death toll was artificially inflated by adding those who passed away from natural causes such as old age.
"No relationship between a colony and the federal government can ever be called 'successful, ' because Puerto Ricans lack certain inalienable rights enjoyed by our fellow Americans in the states", he said in a statement.
Later in August, the aforementioned independent report put the death toll of the 2017 storm at almost 3,000 people - most of whom died after the storm due to complications from widespread power outages and water shortages.
A photographer claimed to have discovered a stockpile of bottled water sitting on a tarmac in Puerto Rico. Then, a few weeks ago, a study from George Washington University revised that number to 2,975. The new report looks at how power outages and medical infrastructure also impacted lives and led to deaths on the stricken island.
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The researchers estimated the number of excess deaths by analyzing death certificates and other mortality data, and comparing the number of deaths during the designated period to past mortality patterns.
The emergency supplies were brought in by FEMA in the aftermath of Hurricane Maria, which smashed the island and left its residents without power, without roofs and without running water.
Trump, who famously DVRs news programs for later viewing, must have finally caught up with the controversy caused by comments he made on Tuesday in which he said his response to Hurricane Maria was "tremendous".
Earlier Tuesday, President Donald Trump had reiterated his praise for the Federal Emergency Management Agency's response.
Ms Cruz shot back: "If he thinks the death of 3,000 people is a success God help us all".
"And when the storm hit they had no electricity, essentially before the storm and when the storm hit that took it out entirely", the president continued.
The administration's efforts in Puerto Rico were widely criticized as slow and insufficient. More than 1 million people already faced mandatory evacuation orders Tuesday in coastal areas of Virginia, North Carolina and SC.