San Juan's mayor has accused US President Donald Trump and his administration of failing in its relief efforts in the aftermath of hurricanes Maria and Jose, saying the White House is "killing us with inefficiency".

Mayor Carmen Yulin Cruz implored Trump on Friday to "make sure somebody is in charge that is up to the task of saving lives", while the president asserted US officials and emergency personnel are working all-out against daunting odds, with "incredible" results.

"We are dying, and you are killing us with the inefficiency," Cruz said during a news conference. "I am begging, begging anyone that can hear us, to save us from dying. This is a people-are-dying story."

The goal is one: saving lives. This is the time to show our "true colors". We cannot be distracted by anything else. pic.twitter.com/7PAINk19xM — Carmen Yulín Cruz (@CarmenYulinCruz) September 30, 2017

Trump has pledged to spare no effort to help Puerto Ricans to recover from the two hurricanes, but has come under great criticism as thousands remain without electricity, water and gas.

The US president lashed out at Cruz in a series of tweets on Saturday, saying the mayor showed "poor leadership".

"They want everything to be done for them when it should be a community effort," Trump said.

Acting homeland security secretary, Elaine Duke, visited the US territory on Friday, surveying the ravaged landscape by helicopter in an hour-long tour, driving past still-flooded streets, twisted billboards, and roofs with gaping holes, offering encouragement to some of the 10,000 emergency personnel she said the US government has on the ground.

READ MORE: Puerto Ricans denounce US hurricane relief efforts

Duke tried, too, to move on from the remarks she made a day earlier in which she called the federal relief effort a "good-news story".

Thousands more Puerto Ricans got water and rationed food on Friday as an aid bottleneck began to ease. By now, telecommunications are back for about 30 percent of the island, nearly half of the supermarkets have reopened at least for reduced hours, and about 60 percent of the petrol stations are pumping.

But many remain desperate for necessities, most urgently water, long after the September 20 hurricane.

Trump is expected to survey the damage on Tuesday.