DOHA, Jan 9 (Reuters) - Daily coronavirus infection rates reported by Kuwait and Qatar have soared past previous peaks recorded in the summers of 2021 and 2020 respectively, as cases rise across all Gulf states. Kuwait on Sunday reported 2,999 new cases of COVID-19, its fourth day of case numbers exceeding a high of 1,993 seen in July last year. Kuwait had seen below 50 daily cases during the last quarter of 2021. Qatar, a small energy-rich state with a population of around 2.8 million, on Saturday reported 3,487 new cases - almost 10% of those tested -- outpacing a previous high of 2,355 seen in May 2020. On Saturday, Qatar reintroduced a set of rules limiting home gatherings to 10 vaccinated people, barring unvaccinated people from entering malls and restaurants and reducing capacity limits for some commercial establishments. Schools in Qatar have reintroduced distance learning until at least January 27. To relieve pressure on Qatar"s testing infrastructure authorities on Wednesday urged travellers and some symptomatic people to take rapid antigen tests, which don"t need to be processed in a laboratory, rather than PCR tests. It also opened a new 10-lane drive-through PCR testing station to sample up to 5,000 people a day. Saudi Arabia, the largest Gulf state with a population of some 30 million, has also seen a rapid increase in cases since the start of the year. The kingdom registered 3,460 new infections on Sunday, still below a peak of more than 4,700 in June 2020. In the United Arab Emirates, the Gulf"s tourism and commercial hub, the past three weeks also brought a surge in cases as the country hosts a world fair during its peak tourist season. Authorities on Sunday reported 2,759 new infections, as it hosts a world fair during its peak tourist season.