Arafat is under enormous pressure to rein in militants
Sheikh Hassan Youssef, a senior Hamas leader in the West Bank town of Ramallah, said: "Hamas is studying the issue of suspending martyrdom attacks.
"It has not been decided yet, but the movement is aware of the interests of the Palestinian people and will take a decision that stems from their higher interests."
Tension between Hamas and the Palestinian security forces erupted into violence in the Gaza Strip on Wednesday night.
The Islamic militants fought a gun battle with Palestinian police who arrived at the home of a senior Hamas leader, Abdel Aziz al-Rantisi, seeking to detain him.
Palestinian leader Yasser Arafat, under international pressure to crack down on militants, called on Sunday for an end to armed conflict with Israel.
Hamas has carried out a string of suicide operations against Israeli targets, including three earlier this month that killed 26 people.
Security talks
Israeli and Palestinian security officials held talks on Wednesday night - the first such meeting since the Israeli Government cut ties with Mr Arafat last Thursday.
But Palestinian officials later said the security meeting was a failure. West Bank security chief Jibril Rajoub told the Associated Press that the Israelis offered no political options.
Israeli forces later withdrew from some Palestinian areas near Ramallah, witnesses said.
Earlier, US Secretary of State Colin Powell telephoned Israeli Prime Minister Ariel Sharon and urged him to help create an environment in which Palestinians can step up their efforts to rein in militant groups.
The BBC's Caroline Hawley in Jerusalem says there is clearly a serious debate about tactics going on among the Palestinian militants.
Our correspondent says much will depend on how the Israelis respond, noting that most Hamas attacks have taken place after Israel has carried out targeted killings of Hamas leaders.
The Hamas leader in Gaza, Mahmoud ez-Zahar, stressed to the BBC that there is a big difference between discussions and a decision.
And in a statement on their official website, Hamas denied they would halt suicide attacks.
Meanwhile, the Palestinian Authority is said to have arrested 15 member of its own security forces, and has closed 33 Hamas offices as part of its efforts to enforce a truce with Israel.
The arrest of the 15 Palestinian policemen is the first time in almost 16 months of Palestinian-Israeli violence that members of the security forces have been accused of taking part in attacks.
Palestinian security spokesman Mohammed Dahlan told AP news agency: "We will arrest anyone who violates Authority decisions."
The BBC's James Reynolds in Jerusalem says the latest measures taken by the Palestinian Authority have apparently been successful in recent days in reducing suicide bomb and mortar attacks on Israel.