The grief-wrenched Texas town of Uvalde on Tuesday began burying its dead from the bloodiest US school shooting in a decade, with funerals for a pair of slain 10-year-old girls who were among the 19 students and two teachers killed one week ago.

Separate memorial services, both closed to the media, were held hours apart for Amerie Jo Garza, remembered for her love of swimming and art, and her classmate Maite Yuleana Rodriguez, an honour student who dreamed of becoming a marine biologist.

So insistent was Amerie’s family on privacy that authorities parked a fire truck outside Sacred Heart Catholic Church to obscure camera shots after the hearse arrived. The girl’s casket was carried inside by six pall bearers in white shirts.

She was buried a short time later during a graveside ceremony at a nearby cemetery. Services for Maite were held the same evening at a Uvalde funeral home.

The two girls were among 19 students, aged 9 to 11, who were shot to death last Tuesday along with two teachers by an 18-year-old gunman who burst into their fourth-grade classroom at Robb Elementary School and opened fire with an AR-15-style semi-automatic rifle.

Several large media outlets in Texas, including the Dallas Morning News and the Texas Tribune, observed 21 minutes of silence on Tuesday — one minute for each of those who died in the attack.

Funerals for the remaining victims are planned over the next two weeks in Uvalde, a town of 16,000 predominantly Latino and Roman Catholic residents, 130km west of San Antonio.

One service on Wednesday will be a joint memorial for Irma Garcia, 48, one of the two teachers killed, and her husband, Jose Garcia, 50, who died of a heart attack two days after the shooting.

The couple, who were high school sweethearts, are survived by four children.