SANAA (Reuters) - Thousands of Yemenis took to the streets of Sanaa Thursday to demand a change of government, inspired by the unrest that has ousted Tunisias leader and spread to Egypt this week. Reuters witnesses estimated that around 16,000 Yemenis demonstrated in four parts of Sanaa in the largest rally since a wave of protests rocked Yemen last week, and protesters vowed to escalate the unrest unless their demands were met. The people want a change in president, protesters shouted, holding signs that also demanded improvements to living conditions in Yemen, the Arab worlds poorest country. President Ali Abdullah Saleh, a key ally of the United States in a war against a resurgent al-Qaeda wing based in Yemen, has ruled this Arabian Peninsula state for over 30 years. If the (ruling) party doesnt respond to our demands, we will escalate this until the president falls, just like what happened in Tunisia, said protester Ayub Hassan. A few dozen policemen with batons silently watched the protests, which ended calmly as demonstrators left to chew qat, a mild stimulant leaf widely consumed in Yemen in the afternoon. Yemens ruling party ran a competing pro-government protest that gathered only a few hundred supporters, witnesses said. Yemen, in the shadow of the worlds top oil exporter Saudi Arabia, is struggling with soaring unemployment and dwindling oil and water reserves. Almost half its 23 million people live on $2 a day or less, and a third suffer from chronic hunger. Current unrest appears to be partly a reaction to a proposal floated late last year by members of Salehs ruling party, the General Peoples Congress, to end presidential term limits that would require Saleh to step down when his term ends in 2013. Yemens opposition coalition tried to rally against the idea in December, but failed to bring large numbers to the street. The wider support for recent protests is apparently influenced by Tunisias successful revolt. Meanwhile, Egyptian police fought protesters in two cities in eastern Egypt on Thursday and prominent reform campaigner Mohamed ElBaradei headed back to the country to join demonstrators trying to oust President Hosni Mubarak. Police fired rubber bullets, water cannon and tear gas at hundreds of demonstrators in the eastern city of Suez, on a third day of protests calling for an end to Mubaraks 30 year-old-rule, a witness said. Across the eastern city of Ismailia, hundreds of protesters clashed with police, who dispersed the crowds with tear gas. ElBaradei told Reuters before he left Vienna for Egypt to join in demonstrations that it was time for Mubarak to step aside. He has served the country for 30 years and it is about time for him to retire, ElBaradei, the Nobel Peace Prize-winning former head of the UN nuclear agency, said. Tomorrow is going to be, I think, a major demonstration all over Egypt and I will be there with them. ElBaradeis arrival could spur protesters who have no figurehead, although many activists resent his absences in recent months. Egyptians torched a police post in Suez early on Thursday in response to the killing of three demonstrators earlier in the week, a Reuters witness said. Police fled the post before the protesters burned it using petrol bombs. On Wednesday evening, people in Suez had set a government building and another police post on fire and tried to burn down a local office of Egypts ruling party. The fires were all put out before they engulfed the buildings but dozens more protesters gathered in front of the partially burned police post later on Thursday morning. A Twitter entry called for a march at 3 pm (1300 GMT) on Thursday in Giza, an area of Cairo. In recent days, people have burned tyres and hurled stones at police in the city centre. The anti-government protests, unprecedented during Mubaraks rule of a state that is a key US ally, have seen police fire rubber bullets and teargas at demonstrators throwing rocks and petrol bombs.