Gov. Ned Lamont\u2019s administration says it plans to continue purchasing and distributing at-home COVID tests throughout the state even as the federal government has begun accepting orders to ship up to 1 billion kits directly to Americans in their homes. The ambitious home-delivery effort \u2014 launched one day ahead of schedule on Tuesday \u2014 comes amid a nationwide shortage of available rapid at-home test kits, which have been largely cleared from store shelves in Connecticut since the omicron variant began its pre-holiday surge. To address that shortage, Lamont\u2019s administration set out in late December to purchase large-scale shipments of tests to distribute through government agencies, churches, nonprofits and municipal test drives. Despite early stumbles in that effort, the state had distributed 3.1 million tests through Thursday, the governor\u2019s office said, with another 500,000 likely to be distributed this weekend. A spokesperson for the governor said that effort will continue, even as the larger federal distribution announced by President Joe Biden is expected to ease the worst of the testing shortage. \u201cWe anticipate that in the future, self-tests will also become easier to find at your local pharmacy, and we are also pleased that the federal government has received a supply of self-tests that families can easily order for free online,\u201d said Lora Rae Anderson, a spokesperson for the governor\u2019s office. The state Department of Public Health on Friday reported an another 4,444 cases of COVID-19, with a daily positivity rate of 13.69 percent, a slight uptick from the previous day\u2019s report. While the number of patients hospitalized with COVID in Connecticut declined again on Friday, nearly half of them have been vaccinated, the state data shows. The total number dropped by 38 to 1,695 \u2014 the lowest since Jan. 5, but about 43 percent of them were vaccinated. Even as the federal government began rolling out plans to ship millions of tests in the coming weeks, the Biden administration is putting pressure on test manufacturers to increase production to avoid future shortages, Bloomberg reported. The initial order of tests made available for delivery this week numbers 500 million, according to the Biden administration, enough for four free tests to be delivered to every household. Another half-billion tests will be available at a later date, the administration said. Lamont on Thursday expressed optimism that the efforts of both the federal and state government to distribute tests would lead to wider availability in the future. \u201cI\u2019d like to think that the supply chain issue is not as big an issue right now, and I think it will only get better, \u201d Lamont said. Dr. Scott Gottlieb, a former commissioner of the Food and Drug Administration who serves on the board of Pfizer, also weighed in during the governor\u2019s press conference Thursday to predict that at-home testing and drug prescriptions will be more readily available later this year. \u201cCome this fall, I think that we should have a situation where there is a large supply of diagnostic tests, these are widely accessible, yes you will be able to self-diagnose at home,\u201d Gottlieb said. Meanwhile, users flocked to the White House\u2019s newly-launched website for ordering tests, where some have reported having issues getting them delivered to buildings with multiple units. Other signs of a limited supply of tests continued to linger. Major retail pharmacies like CVS and Walgreens continued to place caps on the number of testing kits available for purchase at one time, as national demand continues to cause shortages at some stores, representatives for those companies told Hearst Connecticut Media \u201cWe continue to work around the clock to secure additional OTC COVID-19 tests from our vendors and to get those tests on the shelves of our CVS Pharmacy stores\u201d Tara Burke, a CVS spokesperson, said in an email. Mark Kidd, the laboratory and scientific director for Wren Labs in Branford, said demand for PCR tests at their four public testing locations has started to wane since reaching its peak around the holidays. During that peak, Kidd said the lab was processing nearly 5,000 tests a week, a number that has since dropped to 2,000 tests a week. However, Kidd said some of the drop-off is due to two of the lab\u2019s test sites closing for several days last week during cold weather. Prior to the winter surge in the virus, Kidd said the lab was testing about 1,500 tests a week. Even with the federal government shipping rapid testing kits directly to people\u2019s homes, Kidd said he did not foresee demand for laboratory testing falling back to those earlier levels, noting their greater level of accuracy when compared to at-home test kits. \u201cPeople want peace of mind, the PCR tests provide that peace of mind,\u201d Kidd said. Lamont\u2019s administration did not say Thursday how long it planned to continue making its own deliveries of at-home tests. Anderson said the state will \u201ccontinue to follow every lead that comes across our desk in order to support the health and safety of our residents.\u201d That includes Jack Rubenstein LLC, the Glastonbury wholesaler that was originally supposed to ship 500,000 test kits to the state before New Year\u2019s Eve, only for the shipment to fall through. Anderson confirmed on Thursday that the state has since acquired tests from the company, though she did not specify how many.