Agencies quoted Shalom as saying on Monday that there is no place for Hamas in Palestinian politics as long as the group remains armed.
The Palestinian resistance group, which has carried out dozens of bombings in Israel, killing hundreds, is contesting the 17 July Palestinian legislative elections.
While it is honouring a ceasefire between Israel and the Palestinians, it has rejected calls by Palestinian leader Mahmoud Abbas to disarm after the vote.
Hamas is expected to do well in the vote after a strong showing in local elections last week, though it appears unlikely that it will defeat Abbas' dominant Fatah movement.
Meanwhile, Israeli Prime Minister Ariel Sharon has said he will delay a pullout from Gaza for a month, until mid-August, after a religious mourning period.
In an interview with Israel TV on Monday in advance of Israel's independence day, Sharon said: "The evacuation will be carried out, giving consideration to the mourning period," which ends on 14 August."
Sharon says he will delay Gaza
withdrawal until mid-August
Shalom, on the other hand, spoke at a public appearance at a Jerusalem hotel with Palestinian Interior Minister Nassr Yousef.
"I think the Palestinian Authority should do everything possible to prevent Hamas running for election unless it cancels its military wing," Shalom said.
"We must all reject the inclusion of Hamas in the Palestinian political system. There is no place, nor can there ever be, in a democratic society for a political party which bears arms."
Shalom questioned what would happen if Hamas won the election. "Would there be any way to negotiate peace when their main goal is the destruction of Israel?
"Would there be any way to go ahead with disengagement?" he asked, referring to the Gaza pullout plan.
For his part, Palestinian minister Yousef implied that by entering politics, Hamas was tacitly accepting the interim peace accords with Israel which created the Palestinian government.
"We must all reject
the inclusion of Hamas
in the Palestinian political system"
Israeli Foreign Minister
"Hamas knows this election is based on Oslo and the road map," he said, referring to the accords and a current peace plan.
"Hamas knows that important changes have taken place."
Later on Monday, Palestinian Minister for Civil Affairs, Mohammad Dahlan, responding to Shalom and Sharon's statements, told Aljazeera these were not surprising considering that Israel's planned withdrawal from Gaza was a unilateral move anyway - a decision taken without consultation with the Palestinians.
"If the Israelis do not withdraw from Gaza, it would show that they are sliding back to the circle of violence," he said.
Separately, Israeli Vice Premier Shimon Peres has warned that destroying Jewish settlers' homes in Gaza could jeopardise the planned Israeli pullout from the area this summer.
Peres told The Jerusalem Post daily that destroying the homes would lengthen the pullout process by three months, because Israel would be obliged under international law to remove the rubble, at a cost of tens of millions of dollars.
"This alone can spoil it," he said.
Israeli officials are expected to decide what to do with the homes in the coming weeks.