"The occupation's (Israel) statements about Hamas helping IS are stupid accusations... And propaganda that aims to incite against Hamas," spokesman Sami Abu Zuhri told AFP, referring to the Islamic State group, whose fighters carried out the attacks.
"Hamas has made efforts and taken stated measures to secure the border" between the Gaza Strip, which it controls, and Egypt's Sinai Peninsula, he said.
"We are intent on (preserving) Egypt's security."
Israeli Major General Yoav Mordechai said in an interview in Arabic with Al-Jazeera television Thursday that Hamas had provided help to "groups supporting IS" for the attacks, claiming also that wounded jihadists had been smuggled into Gaza.
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There have however been growing tensions between Hamas and extremist splinter groups in Gaza, including those claiming links to IS.
Such tensions have deepened since last summer, when Israel and Hamas fought a deadly 50-day war in and around Gaza.
The extremists have made no secret of their disdain for Hamas over its observance of a tacit ceasefire with Israel and its failure to implement Islamic law.
Gaza militants who said they supported IS claimed responsibility for three separate attacks in May, including a rocket attack on a base of Hamas's armed wing.