Sufa crossing opened to goods traffic, but Karni remains closed.
Last week, Hamas called for other Palestinian factions in Gaza to abide by the ceasefire and said it would take “necessary measures” against violators.
The rocket attacks on Thursday threatened the ceasefire, with Israel shutting Gaza’s goods crossings for four days and Hamas charging that Israel was not keeping to its part of the truce deal.
But the Sufa commercial border crossing reopened on Sunday, the third Gaza crossing opened by Israel as part of the deal.
The Nahal Oz fuel terminal reopened on Friday after being shut for two days.
Officials say there have been no security violations in the past 24 hours.
In addition to the opening of Sufa, Israeli officials had said Karni crossing would be reopened but later reconsidered.
Peter Lerner, an Israeli spokesman, said: “We finally decided to only reopen Sufa for the time being.
“Around 80 trucks filled with goods and humanitarian aid should be authorised to enter the Gaza Strip on Sunday.”
Al Jazeera’s Ayman Mohyeldin, reporting from Gaza, said five trucks carrying gas, petrol for cars and fuel for the territory’s power station were allowed to enter the Nahal Oz terminal early on Sunday.
“It’s a very tricky game as to what comes first, whether the rocket fires or the border closures, but as we see today, there is some movement in the absence of violence,” he said.
UN sources say that since the truce started, Israeli forces have fired into the Gaza Strip at least eight times, wounding two people.
In the occupied West Bank, which is not covered by the ceasfire deal, a Palestinian teenager was killed by Israeli forces on Sunday.
According to Palestinian security forces, 17-year-old Mohammed Doraghmeh was among a group of youths throwing stones at Israeli soldiers in the northern town of Tubas.
Israeli military sources said soldiers opened fire because they spotted a Palestinian who was about to throw a petrol bomb.
Islamic Jihad had warned it might retaliate to Doraghmeh’s attack in the West Bank, however, Ghazi Hamad, a Hamas spokesman, told Al Jazeera that Islamic Jihad would abide by the truce.
“There were some meetings between Hamas and other Palestinian factions, including Islamic Jihad … and they said frankly, this is the national consensus and we have to respect it,” he said.
“The situation is still difficult because not all the crossings are yet open. Essential items … still come in drop by drop,” Hamad said.