Nine months after the U.S. began rolling out vaccines, 73 percent of the population aged above 12 have received at least one shot, and 63 percent have been fully vaccinated.
But health officials have not yet begun to vaccinate children under 12, who account for some 15 percent of the population.
This is a cause for worry for many parents who fear their children could contract and spread the coronavirus.
Kim Tuyen of Houston City, Texas, said: "My first child is eight years old and the second one is just a month old. Both are not old enough to be eligible for Covid-19 vaccines. This makes me really worried."
The U.S. Food and Drug Administration (FDA) approved the Pfizer vaccine for children aged 12-15 in May.
The Moderna vaccine is now awaiting approval for use on children aged 12-17, and the FDA could soon give the green light, Business Insider magazine said.
Both Pfizer and Moderna began clinical trials on younger people in March, and the results of their studies have not yet been published.
Pfizer is expected to have data on the effectiveness of the vaccine for the 5-11 age group by the end of September.
Scott Gottlieb, a former FDA commissioner, said the agency could "green light" vaccination of children under 12 in late fall or winter.
Tuyen said she supported immunization of children. "Pregnant women and children are the subjects that need more protection."
She said she had received a Moderna vaccine and would get a second one in two weeks’ time. Vaccines make her feel more secure after the pandemic recently came roaring back in the U.S.
The world's worst affected country has reported more than 41.5 million infections and 673,000 deaths. With the emergence of the Delta strain, the number of infections has increased sharply to more than 100,000 cases per day.
Dr Anthony Fauci, the nation's top infectious disease expert, said Thursday the high infection rate could somewhat hinder plans to return to normal life.
Phuong Nguyen, who lives in the city of Sugar Land, Texas, said: "I have two children, three years old and one and a half years old. If the vaccination plan is approved, I will have them vaccinated."
He said he is quite worried since the Delta variant spreads rapidly.
The number of new infections in Texas in the seven days through September 9 averaged more than 19,000, up 16 percent from two weeks earlier, while the number of deaths increased by 36 percent, according to the New York Times.
Texas has recorded more than 3.78 million infections and nearly 59,500 deaths since the outbreak first began.
So far 70 percent of its population has had at least one vaccine shot and 59 percent have got two.
"Many people do not believe in vaccines and do not even believe there is a pandemic," Tuyen said.
Tuyen added that she and her family also often wear masks, keep a safe distance from other people and limit going to crowded places to avoid the risk of infection.
Besides encouraging people to get vaccinated – including by offering inducements like $100 -- the U.S. government is also mandating more stringent requirements to combat the Delta strain.
It will require companies with 100 or more employees to vaccinate all of them and conduct weekly Covid tests. This is expected to affect around 80 million people.
President Joe Biden said: "My message to unvaccinated Americans is this: What more is there to wait for? What more do you need to see? We've made vaccinations free, safe and convenient.