Noah Pozner and Jack Pinto, both aged six, will be buried after ceremonies at 13:00 local time.
Twenty children and six women died in the assault on Sandy Hook school by a lone gunman who then took his own life. He had earlier killed his mother.
On Sunday President Barack Obama told residents at a vigil in Newtown the US must do more to protect its children.
He said he would use the powers of his office to prevent a repeat of the tragedy, adding that the nation shared the townspeople’s grief.
“We can’t tolerate this anymore,” Barack Obama said.
“These tragedies must end and to end them we must change.”
He made no specific mention of new gun control measures.
Meanwhile, West Virginia Senator Joe Manchin, who supports gun ownership and has been given an “A” rating by the National Rifle Association, told US network MSNBC that it was time to “move beyond rhetoric” on gun control.
Joe Manchin, a gun owner and frequent hunter, said: “I’ve never had more than three shells in a clip. Sometimes you don’t get more than one shot anyway.
“It’s common sense. It’s time to move beyond rhetoric. We need to sit down and have a common sense discussion and move in a reasonable way.”
Joe Manchin is the first NRA-backed US senator to speak out since Friday’s killings.
In Connecticut, Jack Pinto will be buried in the Newtown Village Cemetery, and Noah Pozner will be buried at the B’Nai Israel Cemetery in the nearby town of Monroe, according to local media reports.
The family of James Mattioli, six, is also holding a wake on Monday.
Other victims’ funerals will be held throughout the week.
Jack Pinto was described as a sports lover, and reports say he may be buried in the No 80 jersey of his idol, New York Giants football player Victor Cruz.
Cruz played in a game on Sunday with the boy’s name written on his shoes and gloves.
Noah Pozner was the youngest victim of the shooting, described by his family as inquisitive and mature for his age.
The parents of Jessica Rekos have spoken for the first time. In an interview with TV network ABC, they said “she was the family CEO, she was the boss”. Her funeral takes place on Tuesday.
And the family of Victoria Soto, a teacher killed at Sandy Hook, called her “the queen” of her family as they recalled her in an interview with CBS News.
“She was the best daughter any mother could ask for,” her mother, Donna Soto, said.
Victoria’s sister Carly, whose shocked expression was captured by a news photographer on Friday and published around the world, said the image already served to renew the hurt.
“It’s like a reminder of that moment all over again, and it kills,” she said.
On Monday, Lt Paul Vance said police continued to do everything they could to answer every question about the shooting.
He said that two people who had been wounded but survived the shooting would be key witnesses and would be interviewed at an appropriate time.
Children who witnessed the attack would also be interviewed – in the presence of parents and professionals – Lt Vance added.
Gunman Adam Lanza, 20, did not seem to have had run-ins with the police, he said, and gave no information about whether mental health professionals had come forward with information about him.
As well as remembering the dead, the community is getting ready for the start of the school week, with teachers struggling to know what to tell their students.
All 20 children who died in the shootings – eight boys and 12 girls – were aged between six and seven, according to an official list of the dead. The school’s head teacher, Dawn Hochsprung, was among those killed.
All victims were shot several times, some of them at close range.
Adam Lanza shot his mother -reportedly in the head – before driving to the school in her car, authorities said.
Officials say he was armed with hundreds of rounds of ammunition, and used a semi-automatic rifle as his main weapon. He was also carrying two handguns, and a shotgun was recovered from a car.
Barack Obama made an appeal for “meaningful action” against gun crime in the US shortly after the attack on Friday.
Sunday saw two senior US Democrats call for stricter gun control.
Connecticut Governor Dannel Malloy said his state had an existing ban on assault weapons, but the lack of a similar law at federal level made it difficult to keep them out of the state.
And Senator Dianne Feinstein, who represents California in the upper house of Congress and is a long-term supporter of stricter gun control, said she would introduce a bill to ban assault weapons.
But opponents of gun control have hit back, saying a ban would be ineffective.
“Having a ban isn’t going to make the very people we would like to prevent from having them, [stop] having them,” said Independent Firearm Owners Association president Richard Feldman.
“They are already owned by tens of millions of people. What is the government planning to do? Come and get the guns? I don’t think so.”
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