A spokesman for the group said the thwarted attack was meant to send a signal that the group had no intention of abiding by the platform of Abbas's new government in the occupied West Bank.
Spokesman Abu Thaer said: "Our message is that the Zionist occupation is continuing its aggression and therefore the resistance will continue."
"We tell Fayyad that his platform is a political platform. Palestine was occupied militarily and we will liberate it militarily," the spokesman added.
A statement issued by Islamic Jihad said: "If Fayyad rejects the choice of resistance, he should pick another people to represent."
|Fatah have rallied in the West Bank|
Led by Salam Fayyad, the Palestinian prime minister, the new government dropped the phrase "armed resistance" from its platform on Friday, angering Hamas in Gaza, where Abbas lost control of the coastal strip last month when Hamas routed his secular Fatah forces.
Abbas responded by sacking a Hamas-led government and appointing Fayyad's.
In a bid to bolster Abbas, Israel has recently renewed a measure of security cooperation with his forces in the West Bank, agreed to stop pursuing some 180 wanted Fatah fighters and released 255 Palestinian prisoners from its jails.
Under a deal between Israel, Egypt and Fayyad's government, thousands of Palestinians who have been stranded in Egypt since Hamas's takeover on June 14 will be allowed back into Gaza starting next week, Palestinian officials said on Saturday.
A Palestinian source familiar with the deal said the Palestinians would start crossing the border in stages starting as early as on Sunday. They will cross from Egypt into Israel and then enter into Gaza.
Israel Radio reported that an initial party of 100 people would be allowed to return on Sunday with the rest to follow later.