"I am done being polite".
"I am not going to be distracted by small comments, by politics, by petty issues". "I am mad with rage", she added.
In a series of tweets Saturday, Trump accused the mayor of "poor leadership" and want the government to do everything for them.
The Trump administration has come under fire from critics who say it is failing to help the island as it struggles with widespread power outages, collapsed infrastructure and ongoing shortages of water and supplies.
Trump resumed his Twitter tear on Sunday, writing that responders have "done a great job with the nearly impossible situation".
"I am asking the president of the United States to make sure somebody is in charge that is up to the task of saving lives".
Cruz said she wanted to "make sure somebody is in charge that is up to the task of saving lives", while the president asserted that USA officials and emergency personnel are working all-out against daunting odds, with "incredible" results.
FEMA announced that Puerto Rico and the US Virgin Islands have received 6.5 million liters of water and 4.4 million kids meals.
Cruz on Friday pushed back on Acting Department of Homeland Security Secretary Elaine Duke's characterization of recovery efforts in Puerto Rico as a "good news story".
Many others have also jumped onto Twitter to criticize Trump, particularly after his latest "ingrate" tweet.
"Well, maybe from where she's standing it's a good-news story", said the mayor, who has been pleading for help since Maria hit Puerto Rico more than a week ago.
"Trump" turned down helping Puerto Rico because it had not paid its bills, adding that he has to worry about America first.
Scarborough also reposted tweets of his fellow "Morning Joe" co-host Mika Brzezinski, saying that Trump is "not fit" to be president. Victims from Hurricane Harvey and Hurricane Irma received immediate aid from federal workers, but Puerto Rico has not benefitted from the same treatment.
Hurricane Maria made landfall in Puerto Rico as a powerful Category 4 storm on September 20, killing at least 16 people.