A Palestinian rights group said the three were trying to sneak through the fence and called what it said was a drone strike an "excessive use of force".

The three who the Gazan health ministry said were aged 13 and 14 were killed late Sunday near the tense border between the Hamas-run Gaza Strip and Israel.

The Israeli army said they had attempted to damage the fence and "were apparently involved in placing an improvised explosive device adjacent to it".

The Gaza-based Palestinian Centre for Human Rights said its investigations concluded the three approached the area Sunday evening "in an attempt to sneak through the border fence".

It said paramedics who retrieved the bodies on the Gazan side of the fence "confirmed that the children did not have anything (weapons)".

It gave their ages as 14 and 15.

An Israeli army spokesman said Monday he had nothing further to add to the previous statement.

The incident occurred after months of protests and clashes along the Gaza border. Several military flare-ups have also occurred in that time.

The boys were identified by the health ministry as Khaled abu Said, 14, Mohammed Abu Zaher and Mohammed al-Satari, both 13.

They came from the village of Wadi al-Salqa around a kilometre from the border fence.

Hundreds attended the funeral Monday.

Waleed Muharib, 20, a neighbour, said he saw them as they left.

"They were laughing as they headed to the border. I told them to be careful. They said they were going to catch birds."

Later, he said, "I heard the explosion and I knew they were dead".

Ibrahim al-Satari, the father of 13-year-old Mohammed, told AFP he couldn't understand it.

"I do not know why they killed my only son and his friends. These are small children," he said.

"They could have caught them and found out they were playing or hunting."

In their school classrooms Tuesday, teachers marked the boys' seats with notes with their names.

UN envoy Nickolay Mladenov expressed sympathy for the families.

"Such tragedies must be avoided at all costs," he wrote on Twitter.

"Children must be protected, not exposed to violence or put in danger."

At least 218 Palestinians have been killed by Israeli fire in the months of demonstrations and clashes. The latest was shot dead Monday.

One Israeli soldier has been killed along the border since the protests began on March 30.

Israel says its actions are necessary to defend the border and stop infiltrations and attacks, which it accuses Hamas of seeking to orchestrate.

Palestinians and rights groups say protesters have been shot while posing little threat.

Israel and Palestinian militants in Gaza have fought three wars since 2008 and the recent unrest has sparked fears of a fourth.

On Friday and into Saturday, Palestinian militants fired dozens of rockets into southern Israel, which responded with extensive air strikes.