Riad Malki said "Hamas wants instability in the region" and suggested rockets have continued to be launched from the Hamas-controlled Gaza Strip as "a way to interfere" in the Israeli vote.
Israel carried out a bruising three-week offensive in the Gaza Strip last month in an attempt to halt years of rocket fire on southern Israeli communities.
Israel and Hamas announced an informal truce on January 18, but two rockets struck southern Israel on Sunday. There was no immediate claim of responsibility for the rocket attacks.
Malki said the Palestinian Authority – which is at odds with Hamas – is "very much worried" that such attacks might "really push Israeli public opinion and the voters to vote for an anti-peace government."
Polls suggest that after Tuesday's parliamentary vote, Israel's next government could be more hawkish than the current coalition.
Malki also sought to stress that the Palestinian Authority is willing to negotiate with the new Israeli leadership, and he urged all sides not to squander the opening provided by the election of President Barack Obama.
Malki said Obama clearly has decided "to be fully engaged in the process," and noted the president's telephone call to Palestinian counterpart Mahmoud Abbas shortly after Obama's election victory, as well as his decision to dispatch George Mitchell as the new special US envoy to for Middle East peace.
"We hope that all these signs should be really invested in the right direction to promote peace in the region," Malki said.
"We, as the Palestinian Authority, are ready to be fully engaged in order to put an end to the Israeli occupation of our own territory and to establish an independent Palestine state."
Islamic Jihad: Barak, Bibi Livni all enemies
Meanwhile, a spokesman for al-Quds Brigades, Islamic Jihad's military wing, said Monday that the elections in Israel were of no consequence to his organization.
"We need to understand the racist Zionist mentality," he said. "In our eyes Barak, Livni, and Netanyahu are all enemies, and we don't care which of them gets elected. What we care about is how to face them in the next round."
Abu Hamda added that the Palestinian casualties in Gaza were being taken advantage of by Israeli election campaigns.
"The Zionist enemy continues to praise the concept that states that a seat in government can be reached at the expense of Palestinian blood," he said.
"What happened during the recent war is part of the elections battle in Israel. There were individuals who wanted to better their electoral situation by killing women and children, and destroying homes and mosques."
Ali Waked contributed to the report