PRAGUE, Nov 15 (Reuters) - Hospitals in Slovakia, one of Europe"s least-vaccinated nations, have been filling up with coronavirus patients, with the northeastern region of Presov reporting almost no spare intensive care beds, authorities and hospitals said on Monday. President Zuzana Caputova has signed a law allowing the government to force unvaccinated people to test twice a week before attending work in the worst-affected regions and keep them out of restaurants and other services. The country of 5.5 million was not planning a national lockdown, however. Neighbour Austria imposed a lockdown on unvaccinated people on Monday as winter approaches and infections rise across Europe. Germany is considering tighter curbs and Britain expanding its booster program to younger adults. read more The Slovak Health Ministry said the Presov region had 96% of lung ventilator beds occupied and has had to send 35 seriously ill patients elsewhere over the past week. "Presov region hospitals report critical situation - only 2 beds with lung ventilation are free," the ministry said in a statement. In neighbouring Kosice, the capital of the southeastern region, the main hospital said it was admitting 20-40 patients per day and had nearly 90% of beds full. There were only few high-flow oxygen and lung ventilators left. "It really is serious - deciding who gets the instruments," the Luis Pasteur University Hospital Director Jan Slavik said in a statement. The hospital said 80% of its patients were not vaccinated, and that it had only one fully vaccinated patient to date on lung ventilator. Slovakia has has reported more than 6,500 cases per day in the past week. The country"s total death toll from the pandemic at 13,598. There were 2,637 people in hospitals with coronavirus on Monday, including 241 on lung ventilators. That is still below the peak of 3,800 seen in March. Slovakia had 53.7% of adults vaccinated as of Monday according to data from the European Centre for Disease Prevention and Control (ECDC), below the EU average of 76%. Reporting by Jan Lopatka; Editing by Angus MacSwan