BUCHAREST, Oct 2 (Reuters) - Thousands of people demonstrated in the main squares of the Romanian capital on Saturday against new coronavirus restrictions announced by the government this week to fight a steep rise in infections. Protesters, mostly not wearing face masks, gathered in University and Victory squares outside government offices, holding Romanian flags, blowing vuvuzelas and shouting: "Freedom, freedom without certificates," and "Down with the government." Local media put the number of demonstrators at 15,000. The new measures due to take effect on Sunday include restricting entry to public spaces such as theatres, cinemas, restaurants and gyms to people who can present a digital certificate proving they are fully vaccinated or have had the illness. The number of new COVID-19 infections reached a record high of 12,590 on Saturday and authorities said intensive care units were running out of space. Romania has the second lowest vaccination rate in the European Union, just ahead of Bulgaria. Weekend curfews have been introduced for unvaccinated and the government plans to make inoculations mandatory for healthcare sector"s workers, doctors and nurses. read more The government has also made face masks mandatory in all public spaces in places where the case incidence exceeds 6.0 per thousand people. Bucharest reached a record of 8.28 per thousand new infections over the past two weeks, among the country"s steepest rates. Among the protest organisers was an ultranationalist parliamentary grouping that is hoping, together with other opposition parties, to topple the centrist government on Oct. 5, when a parliamentary vote of no-confidence is scheduled. read more The AUR said on its website: "If they don"t see us, they can"t hear us." Just over a third of Romania"s adult population is fully vaccinated so far, amid widespread distrust in state institutions and misinformation campaigns.