Parts of New York City's crippled subway system will begin operating again with partial service Thursday, with fleets of buses filling in the gaps knocked out by severe flooding, officials said. With some subway tunnels and stations still filled with water, and power still turned off in downtown Manhattan, big holes will remain in the nation's largest public transit system even after trains start rolling. New York Gov. Andrew Cuomo said when he announced the restart Wednesday that there would be no subway service in Manhattan south of 34th Street, an area that includes the city's financial district and many tourist sites. Commuters who would normally zoom beneath the East River on trains would be asked to take shuttle buses instead across a handful of bridges. The Metropolitan Transportation Authority released a "Sandy recovery service" subway map for use starting Nov. 1. "We are going to need some patience and some tolerance," Mr. Cuomo said. But the restarting of many parts of the system was sure to breathe life back into a paralyzed city, and allow millions of people to finally get to their jobs, or to school, for the first time since the system shut down Sunday. Limited service was also to resume at 2 p.m. Wednesday on two of the city's vital commuter rail systems, Metro-North and the Long Island Rail Road. Both of those rail systems, which extend many miles into the Connecticut and Long Island suburbs, had been knocked out by power failures, downed trees, and, in the case of the LIRR, flooding in tunnels beneath the East River. Mr. Cuomo said three of the seven flooded train tunnels beneath the East River had been pumped out, but restoring them to service could take time, as equipment that was submerged in the storm is inspected and repaired. Vehicle tunnels, including the Brooklyn Battery Tunnel and the Queens Midtown Tunnel, also took on huge amounts of water. The Brooklyn tunnel alone had an estimated 70 million gallons of water in it Wednesday morning, the Metropolitan Transportation Authority said. Mr. Cuomo's announcement came as New York struggles to recover from Monday night's storm. Bus service resumed. Flights slowly got back in the air at two major airports and the New York Stock Exchange rang back to life after two days without trading. But large swaths of the city and its northern suburbs—about 1.6 million customers—remain without power. The subways carry 5.2 million riders daily; about 2.5 million people use city buses. The LIRR and Metro-North each has 300,000 daily riders.