Abu Qusai, a spokesman for the Brigades, said: "The rocket attack was in response to Israeli violations. Any calm deal must end Israeli attacks on our people in the West Bank too."
The Israeli army killed two Palestinians in a raid on the West Bank on Wednesday, an attack that the Islamic Jihad movement had already claimed as provocation for the three rockets fired later the same day.
The truce, brokered by Egypt, does not cover the West Bank.
Nour Odeh, Al Jazeera's correspondent in the West Bank, said: "This ceasefire that was reached through Palestinian consensus in the Hamas controlled Gaza; it was adhered to and welcomed by all Palestinian factions.
"Now we have two factions saying that actions in the West Bank must have repercussions," she said.
"The al-Aqsa Martyrs Brigades….says the ceasefire must include the West Bank. This is a departure from the official Fatah statement and will no doubt being a worrying development even for president Mahmoud Abbas."
Israel closed three of its border crossings with the Gaza Strip in response to Tuesday's rocket attacks, and they remained shut on Thursday.
"The Gaza crossings are still closed," Peter Lerner, an Israeli military spokesperson, said before the latest rocket attack.
He said that the restrictions were imposed "in response to the firing of rockets on Tuesday".
The Erez passenger terminal remained open for humanitarian purposes, he added.
Asked when supplies would again be allowed into Gaza, he said: "This will depend on the security situation - there is an ongoing evaluation."
The six-month truce between Israel and Hamas entailed a gradual easing of a blockade that Israel imposes on the Palestinian territory as well as an end to attacks by both sides.
Islamic Jihad vow
After the crossings were shut on Wednesday, Islamic Jihad said that it would abide by the truce but warned it would respond if Israel was seen to have violated the agreement.
"We have confirmed to our friends in Hamas that we have decided to respect the ceasefire," Daoud Shihab, a spokesperson for the group, told the AFP news agency:
"We will apply the pact on the suspension of attacks if Israel also respects it," he said.
He said that a "committee comprising representatives of Jihad, the Popular Front for the Liberation of Palestine, the Democratic Front for the Liberation of Palestine and Fatah will meet when Israel breaches the truce to determine a riposte".
Israel imposed the blockade after Hamas took power of the Gaza Strip in June 2007.
The World Bank says the embargo has crippled the Gazan economy, where about 80 per cent but Israel says it has allowed enough supplies to be transported to the strip.
Meanwhile, Ofer Dekel, an Israeli envoy, is due in Cairo on Thursday to press Egyptian authorities not to reopen the Rafah border crossing until Corporal Gilad Shalit, who was captured two years ago, is released.
Rafah, the only Gaza crossing that bypasses Israel, has been closed since 2006, although Egypt has allowed some medical patients to cross the border.
Dekel is to meet Omar Suleiman, an Egyptian intelligence chief, who played a key role in mediating the truce which came into effect on June 19.
Hamas said on Wednesday that Shalit's release is unrelated to the truce agreement and that he will only be freed in exchange for the release of 450 jailed Palestinians.