CAIRO (Reuters) - Cairo protesters dug in for a long fight on Monday, pressing their demand for an overhaul of the political system and the resignation of President Hosni Mubarak as many Egyptians tried to resume their normal lives. Up to 2,000 people bedded down overnight under blankets and tents made from plastic sheeting in Tahrir Square. Some slept while others camped out on woollen blankets as national and revolutionary songs blared out from loudspeakers. Some slept in the tracks of the armys armoured vehicles to prevent them being used to force the protest into a smaller place to allow traffic to circulate. Makeshift barricades were still up and some burned out vehicles had not been moved. Protesters searched people to ensure there were no trouble-makers entering Tahrir, or Liberation, Square which has come to symbolise opposition to 30 years of Mubaraks rule. Many young men dismissed a dialogue taking place between new Vice President Omar Suleiman and opposition groups as unacceptable, vowing to stay in the square and pursue what has been described as the Nile Revolution. I reject dialogue. We dont recognise this government. Mubarak has to go. The despot has to go, Sayyed Abdel-Hadi, a 28-year-old accountant, said. We will not despair. We will stay until he leaves. We dont want Suleiman, he is a symbol of Mubarak. If he becomes president we will stage another revolt. We have been living for 30 years under humiliation and injustice, Osama Gamal, a 22-year-old teacher, said. We want our rights. We want better education, he added. Amongst the tents in Tahrir, protesters set up food stalls and played traditional music. They also chanted anti-Mubarak slogans and prayed. Elsewhere in Cairo, streets began to clog with familiar traffic jams. Many shops reopened and crowds gathered outside small groceries and vegetable and fruit shops freshly stocked after days of disrupted supply lines. Although the protest movement, now in its 14th day, has yet to secure its key demands, many Egyptians who were not directly involved have followed its lead to try to win what they say are their political rights. Hundreds of Egyptians demanding cheaper apartments rallied outside a government office on Monday, emboldened by mass anti-government demonstrations to press their case. Many stood for hours outside the downtown offices with their application forms. Some said they would join the protest camp if they were not allowed to enter. If you dont let us in, we will head to Tahrir, they shouted. In Alexandria, protesters were on the streets in smaller numbers on Monday but said they planned larger demonstrations for Tuesday and Friday. Shops were mostly open in the Mediterranean second city, where protest numbers have rivalled those in Cairo, as people began to resume their normal lives. A similar pattern was seen in the industrial port city of Suez, which has seen some of the most violent protests, with numbers expected to gather on the streets in the afternoon after banks close and bigger protests planned for Tuesday and Friday. State-run schools and universities remain closed for the week, for the normal mid-year holiday. Amateur footage of apparent police violence against protesters has filtered out into the media. Amateur video broadcast by Al Jazeera shows what it says were images of a protester being shot dead by police in Alexandria on Jan. 28. In an empty street, the man is seen walking slowly towards police officers with his arms outstretched. He then halts and removes his jacket before being shot at a distance of some 10 metres, falling to the ground. Meanwhile, President Mubaraks new cabinet on Monday holds its first full meeting since an uprising started nearly two weeks ago, with no concrete progress in talks with Islamists and an opposition who demand his immediate exit. Mubarak, 82, who has refused calls to end his 30-year-old presidency before September polls, saying his resignation would cause chaos in the Arab worlds most populous nation, has tried to focus on restoring order. Meanwhile, Muslim Brotherhood said on Monday it could pull out of talks with the government if opposition demands were not met, including the immediate exit of President Hosni Mubarak who on Monday chaired a cabinet meeting. We are assessing the situation. We are going to reconsider the whole question of dialogue, the Brotherhoods Essam el-Erian told Reuters on Monday. We will reconsider according to the results. Some of our demands have been met but there has been no response to our principal demands that Mubarak leave. US President Barack Obama said on Monday talks to resolve Egypts crisis were making progress. Obviously, Egypt has to negotiate a path and theyre making progress, Obama told reporters while returning to the White House after a speech to a business group.