Recent weeks have seen a series of increasingly violent thefts by criminal gangs, which aid workers have said are now the main obstacle to the distribution of supplies.
On 16 November, a convoy of 109 lorries carrying food was attacked by masked men who held the drivers at gunpoint before stealing 97 of the lorries.
A notorious Gazan criminal family later blocked the main road leading away from Kerem Shalom for two days, erecting iron barriers and reportedly firing on lorries trying to access an aid distribution point.
Aid workers and locals have also alleged that armed men operate within plain sight of the Israel Defense Forces (IDF) in a restricted zone at the Israel-Gaza border.
Announcing the pause in deliveries, Mr Lazzarini said the road away from the crossing "has not been safe for months", citing the theft of five more lorries on Saturday as well as the incident last month.
The announcement also followed the death of three people employed by World Central Kitchen (WCK), a food charity, and two others in an Israeli strike on Saturday.
Israel said the target of the strike was a WCK employee who had taken part in the 7 October attacks.
"The delivery of humanitarian aid must never be dangerous or turn into an ordeal," Mr Lazzarini said.
He said there had been a "breakdown of law and order" and that the responsibility to protect aid workers lay with Israel.
"They must ensure aid flows into Gaza safely and must refrain from attacks on humanitarian workers," he said.
Israel has in recent months opened a number of other crossings into central and northern Gaza following international pressure to increase the flow of aid, but Kerem Shalom remains the one through which most aid enters Gaza.