Mr Siam said security forces will be given full powers to investigate the clashes, particularly the assassination of a militant commander.
A commission of inquiry was set up late on Friday to probe the attacks, which also left 36 people wounded.
Mr Siam said he hopes clan elders, mosques and local media can contribute towards calming tensions.
“We will ensure that nobody is above the law and demand an end to the instability and armed chaos,” he said on Sunday.
Later addressing a news conference in Gaza City, Mr Siam said he has been in contact with “imams and gunmen” in a bid to control the situation, however warned that it could take months, if not a year, to end the armed chaos.
“I am going to meet the groups, heads of security services until we bring people to face their responsibility,” he said.
Friday’s deadly violence was the first major challenge faced by the new Hamas-led government since its inauguration two days earlier, after it beat Fatah, the party of Palestinian leader Mahmoud Abbas, in elections.
Israel has regularly criticised the Palestinian Authority for failing to bring militant groups to heel.
Mr Said, who only took office four days ago, said security problems would not be solved “by waving a magic wand”.
“The Palestinians, who have seen security chaos and misrule for years, will have to wait a little more, one year.”
He also stressed that the interior ministry would not be composed only of members of Hamas, branded a terrorist organisation by Israel and the West, but rather would be mixed and accorded on a merit basis.
While he again ruled out any security cooperation with Israel on a “national level”, he said he was not opposed to coordinating on daily matters such as water, electricity and health.
Israel has refused to deal with the new Hamas government unless it recognises the Jewish state’s right to exist, renounces violence and commits to past peace agreements.
Meanwhile, Israeli President Moshe Katsav hosted talks to form a new government on Sunday, amid a war of words between the winning Kadima party and the centre-left Labour, its most likely coalition partner.
Mr Katsav met senior members of Kadima, which came out on top in last week’s general election with 29 seats in the 120-member parliament, and formally asked that its Acting Prime Minister Ehud Olmert to take the helm.
“We hope that he can form a coalition as large as possible. One that will permit reconciliation, ensure stability and take decisions,” Roni Bar-On, incoming Kadima MP, told reporters after the talks.
“We also hope that this coalition will stay in place until the end of the legislature in November 2010,” he said.
Mr Olmert has insisted he will be the next prime minister.
But the centre-left Labour, Kadima’s most likely coalition hope, has recommended to Mr Katsav that its leader, Amir Peretz, be charged with forming the coalition cabinet, arguing that Kadima’s narrow victory does not give the party a clear-cut mandate.
Mr Katsav has until April 12 to choose a prime minister, who will then have 28 days to form a government, with the possibility of a 14-day extension, before the new line-up is put to a parliamentary vote of confidence.