Parkland school building where 17 were killed should be demolished: Officials

— -- As two more funeral services were held Sunday for victims of the latest American mass school shooting, authorities told ABC News that a major step toward healing Parkland, Fla., would be to demolish the building where 17 students and teachers were gunned down.

Mourners crowded into Temple Beth El in Boca Raton for a private funeral service for Scott Biegel, the 35-year-old geography teacher shot to death at Marjory Stoneman Douglas High School on Wednesday as he tried to protect students from the gunman.

Earlier, family and friends held a memorial for 14-year-old Alexander Schachter, a freshman and trombone player in the school marching band, at the Heron Bay Marriott in Coral Springs.

Broward County Schools Superintendent Robert Runcie said he and officials believe a fitting tribute to Biegel, Alexander and 15 others killed in the massacre would be tear down the building the shooting occurred and turn the space into a memorial park.

"So I will tell you that we...aren't having any classes held in that building going forward," Runcie told ABC News. "What the ultimate disposition of that building is, we don't have any definitive answer. I can tell you what the aspirations of the community are and I agree with them, is that that building should be demolished and a memorial erected there."

Broward County Sheriff Scott Israel said the bullet-riddled Building 12 at the high school is still a crime scene, where investigators are combing for evidence.

The sheriff, whose department is leading the investigation of the killing spree, told ABC News he agreed that "as soon as humanly possible, that building be destroyed forever."

"Kids shouldn't have to walk by and even look at that building. It's just a stark reminder of the horrific, detestable killings that went on that day," Israel said.

School officials announced Sunday that Stoneman Douglas High School will remain closed through at least Wednesday.

"The goal is to allow staff to return to campus by the end of the week," according to a statement from the Broward County School District.

Israel said three of his children, triplets, all attended Stoneman Douglas High School and had classes in Building 12 when they were freshmen in 2015.

"When I walked through the school for the first time, and I certainly wouldn’t be graphic about what I saw, I don’t think that’s appropriate for TV, but as I started to internalize what I did see, I was imagining three years earlier, when my children were freshmen, being in that same room," Israel said. "It was heart-wrenching."

Four patients injured in the shooting remained hospitalized, all in fair condition, according to Broward Health Systems officials.

Israel said the alleged killer, 19-year-old Nikolas Cruz, is in solitary confinement under suicide watch.

"We always have eyeballs on him," Israel said, adding that Cruz has stopped speaking with investigators.

"The killer has his constitutional rights -- has decided not to speak. He has an attorney, and his attorney has made it clear. So we've stopped the questioning phase," Israel said. "So now the investigation is in the hands of my lab people, my crime [and] CSI people."

Cruz's lawyer, Broward Public Defender Howard Finkelstein, told ABC News he is willing to have his client plead guilty immediately in return for the prosecution agreeing to take the death penalty off the table.

But Israel said he has heard from many people in the community who don't want to see any leniency granted to Cruz.

"I think Howard would tell you that it'll be easier to heal if we don't have a trial and everything that would go with it over a plethora of years," Israel said. "But there are people out there who told me, 'I don't wanna go to bed tonight with him alive.' So the death penalty has to be considered, and that's not my call."

Broward County state attorney Michael Satz issued a statement on Saturday, saying: "This is certainly the type of case the death penalty was designed for."

Meanwhile, White House officials said Sunday that President Trump will host a "listening session" on school safety on Wednesday with students and teachers at the White House, and meet with local and state officials on Thursday to continue discussing the subject.

Some students from Stoneman Douglas High plan to be at the Florida state capital in Tallahassee on Tuesday to meet with state legislators to demand they take action to keep students safe in school.

Student Jaclyn Corin organized the trip and says about 100 students will join her in Tallahassee.

Jaclyn said all of the students are part of the “Never Again” movement spawned by the mass killing at their school and has been spreading across the country via social media.

"It shows that we are mature enough," Jaclyn told ABC News. "We will come at them and do whatever it takes to change the way our state runs and the nation [operates]."