(Adds details on insurance coverage for at-home tests)By Jeff MasonWASHINGTON, Dec 2 (Reuters) - U.S. President Joe Biden on Thursday laid out his strategy to fight the Omicron and Delta coronavirus variants over the winter, including free and insurer-funded at-home COVID-19 testing and new requirements for international travelers. However, a White House official late on Thursday said the government will not reimburse private health insurers for the cost of at-home tests. The largest U.S. employer-based health insurers include Cigna Corp, UnitedHealth Group and CVS Health Corp. Currently, insurers are reimbursed a set amount by the government for most medically necessary COVID-19 tests performed in labs and medical offices. Evercore ISI analyst Michael Newshel said the strategy could come at a notable cost for health insurers, with the coverage requirement possibly lasting through the first half of the year.