The creation of such forces has intensified fears among many Palestinians of violence between feuding factions that could destabilise a chaotic security set-up.
Eighty men drafted from disparate Fatah cells jumped over burning tyres and performed other drills in the Gaza Strip, where internal tensions have mounted since Israeli forces and settlers withdrew last year.
Hamas crushed Fatah, owing allegiance to Mahmoud Abbas, the Palestinian president, in January elections, only to be shunned by the West after taking power. The aid cut-off that followed has deepened poverty in Gaza and the occupied West Bank, spreading rancour that has erupted into street battles.
Saeed Seyam, the interior minister and a senior Hamas official, last week mobilised 3000 new paramilitary police in what he called a move to crush lawlessness and oust Palestinian squatters from evacuated Jewish settlements.
But some in Fatah suspected that the move was intended to consolidate Hamas's power and control over dwindling Palestinian resources.
"We formed the new force in a challenge to the force Hamas had formed and which we regard as illegal," Al-Mua'tasem Billah, a spokesman for the new Fatah militia, told Reuters on an impromptu military training ground in the Rafah refugee camp.
"We do not wish to clash (with Hamas-led police), but if it happens, we will not stand handcuffed," he said as gunmen took aim and fired at targets in the distance.
Factional clashes wounded 30 people last month after Abbas, who wants to revive peace talks with Israel, rejected Hamas's appointment of a leading Gaza militant as a senior Palestinian security chief.
Abbas has vetoed the paramilitary
police raised by Hamas
Abbas also vetoed the new Hamas militia, which Seyam later said would be part of the regular police contingents.
Hamas, sworn to Israel's destruction, helped lead a Palestinian revolt that erupted in 2000 but has largely abided by a ceasefire for more than a year.
Billah accused Hamas of sponsoring some armed groups that have set up camp on farmland largely unused since Israel uprooted 21 settlements in coastal Gaza.
"If they (Hamas) are serious about restoring law and order, let them dismantle their training camps and leave the liberated land and all the others will follow," Billah said.
Among tactics acted out by the Fatah militiamen were gun attacks, ambushes on cars, and the release of hostages.
"The (Fatah) force will be assigned to protect Fatah's sons and Fatah's institutions against attacks, whether from Israel or from parties inside the home," he said.
Meanwhile, Goeran Persson, the Swedish prime minister, on Wednesday said two leading Hamas officials hoping to visit Sweden this month would not be allowed entry after France denied them a visa.
"We have no national interest in inviting them (Hamas) and are therefore going to follow the line that the Hamas leader will not be issued with a visa for Schengen countries"
Goeran Persson, Sweden's prime minister
Sweden and France are signatories to the so-called Schengen accords between EU members and others, which grant freedom of travel within their borders to visitors having obtained a visa from any other member country.
Salah Muhammad al-Bardawil, Hamas parliamentary group spokesman, and Mohammad al-Rantissi, a Hamas official, were to visit Malmo in southern Sweden on May 16 after an invitation by a local association.
“We have no national interest in inviting them (Hamas) and are therefore going to follow the line that the Hamas leader will not be issued with a visa for Schengen countries," Persson said during a visit to Finland.
The French foreign ministry on Wednesday confirmed that it had refused visa applications for both Hamas officials.
Members of the Swedish parliament had also been planning to meet the two men in Sweden, but the Swedish government has said none of its members would do so.
Sweden, in line with the rest of the European Union, does not have political contacts with the Hamas-led Palestinian government.
Hamas is listed by both the EU and the United States as a terrorist organisation, and both have frozen assistance to the Palestinian Authority.