"The Mayor of San Juan, who was very complimentary only a few days ago, has now been told by the Democrats that you must be nasty to Trump", Trump wrote on Twitter Saturday.
Trump responded on Saturday by claiming Cruz has "poor leadership".
Cr Cruz has criticised the federal relief effort generally for being too slow and too little.
Carmen Yulin Cruz, the mayor of Puerto Rico's capital city, San Juan, had accused the Trump administration of failing the USA territory.
In addition to all that, I think we can all agree that saying "nasty" things about Trump isn't exactly a grand conspiracy that needs to be masterminded by the likes of Chuck Schumer and Nancy Pelosi.
Following the devastating hurricane that ripped through Puerto Rico earlier this month, Kim Kardashian took to Twitter to shut down Donald Trump after his comments to the victims of the natural disaster.
This follows Cruz's tearful plea to the government to help on Friday, standing in front of palettes of food and water donated by other people.
The US President has slammed the San Juan Mayor.
Honoré made his remarks during an interview on CNN Newsroom. And you called the best person for the job. Let me just say, I wish all of you could come here, I wish there was video you could see of people cleaning out their homes with nothing.
"Dammit, this is not a good-news story", Cruz said. General Jeff Buchanan. Cruz has been out in San Juan's flooded streets, locating survivors, speaking to residents and handing out supplies. "This is a story of a devastation that continues to worsen".
Aid workers prepare to deliver generators.