The protest came two days after an MP loyal to Mubarak said demonstrators should be shot at because they pose threat to the national security .
“I would have questioned the interior ministry for being soft on these outlaws,” Nashaat al-Qasas told Egypt’s parliament.
“Do not use water hoses to disperse these outlaws, shoot at them directly.”
The independent al-Shorouk newspaper had also quoted Hamid Rashid, an aide to the interior minister, as saying that “the law permits police and security forces to use force and open fire on protesters if they disrupt national security”.
The protesters at Tuesday’s demonstration shouted for police to fire on them and held aloft placards reading “shoot us”.
“The ruling party is a party of sticks and bullets,” they chanted.
Activists also filed complaints to the state prosecutor general against the ruling party politicians who had called for the use of force, citing a law against incitement.
Iman, a Sixth of April movement protester, told Al Jazeera: “It is degrading. Why are we a threat to national security? Because we are calling for the country to be better?
“I’m not afraid to be here it is my right to protest. And if they consider shooting us then fine.”
Qasas later backed away from his statement and Safwat el-Sherif, a senior NDP official, said the party backed Egyptians’ right of expression and condemned all calls for violence or shooting.
Sherif also said he trusted the police’s ability to deal with wisdom and restraint, state news agency MENA reported.
Protests have been rare in Egypt but briefly gained momentum around the first multi-candidate presidential vote in 2005, when Washington was pushing for more democracy in the Middle East.
Rights advocates say security forces have used rubber bullets and tear gas to quell protests in the past, methods they say are meant to crush dissent and keep the government in power.
An emergency law instated after the assassination of President Anwar Sadat in 1981 gives authorities scope to detain people indefinitely under the banner of national security.
Washington has criticised Cairo’s handling of the protesters, but Egypt, one of the biggest recipients of US foreign aid, has dismissed the comments as interference.
While the NDP is expected to win a huge majority in parliament, Mubarak has not said if he will run again. Even if he steps down, many Egyptians say the 81-year-old, who recently underwent surgery, will try to hand power to his son, Gamal.
Mohamed ElBaradei, former head of the UN nuclear watchdog, could shake up the race if he runs.
Ayman Nour, an opposition politician who was imprisoned for alleged forgery after challenging Mubarak in 2005 polls, said Qasas should be tried for inciting violence.