The track of Hurricane Henri appears to be shifting slightly more east on Saturday night.

Landfall now appears possible on far eastern Long Island or southern New England, anywhere from eastern Connecticut to Rhode Island to southeastern Massachusetts on Sunday afternoon. Earlier in the day, it appeared as though the storm might hit central Long Island.

The storm was moving quickly -- 21 mph -- and still maintaining hurricane strength.

Henri is expected to either be a weak hurricane or strong tropical storm on Sunday morning or early afternoon as it moves over or just east of Long Island and eventually into southern New England through the day on Sunday.

Rail service in parts of New York and Connecticut will be halted Sunday due to Henri.

The Long Island Rail Road will be suspending service east of Patchogue on the Montauk Branch and on the Greenport line.

Metro-North, which serves New York and Connecticut, will be suspending service on the Wassaic Branch of the Harlem Line and on the entire New Haven Line, including the New Canaan, Danbury and Waterbury branches.

In Connecticut, service on the rail lines Shore Line East and Hartford Line is suspended starting Sunday "until further notice."

Amtrak also announced it would be canceling all Northeast Corridor service, including Northeast Regional and Acela, between New York and Boston on Sunday.

Flight cancellations are also expected in the region.

"Port Authority expects flights to be canceled," Gov. Andrew Cuomo said during a briefing Saturday. "Obviously I would check with your airline before you go to the airport tomorrow into Monday, maybe Tuesday."

New York City Mayor Bill de Blasio defended continuing on with its "We Love NYC Homecoming Concert" Saturday evening, as the city prepares for Hurricane Henri.

"Since the real impact is not expected until well after the concert, we believe absolutely we can do both these things at once," de Blasio said during a press briefing Saturday, as the concert was set to kick off in Central Park with performers including Bruce Springsteen and Patti Smith.

The mayor urged concertgoers to go straight home at the end of the night. "If you're going to the concert ... go home right after and get ready for tomorrow," he said.

De Blasio, who declared a state of emergency for NYC earlier on Saturday, said the city is preparing for heavy rain, wind and downed trees.

-ABC News' Matt Foster

President Joe Biden held a call with the governors of six northeastern states Saturday to discuss Hurricane Henri, the White House said.

The governors are working with Federal Emergency Management Agency and the National Guard to prepare for possible "widespread power outages, coastal storm surge, and inland flooding," the White House said in a statement.

FEMA has pre-positioned over 700 response personnel, meals, tarps and generators in the region.

"On the call, the President made clear that states have the full support of the Federal government to aid local emergency response efforts," the White House said.

Those on the call included New York Gov. Andrew Cuomo, who is in his final days of office after resigning earlier this month following sexual harassment allegations. His successor, Lt. Gov. Kathy Hochul, also joined the call, along with the governors of Connecticut, Massachusetts, Maine, New Jersey and Rhode Island.

National Grid said it is deploying over 4,000 personnel in Rhode Island and Massachusetts to restore power to affected areas.

As of 5 p.m. Sunday, approximately 72,600 customers in Rhode Island and 8,500 in Massachusetts were without power, according to the utility.

"The hardest hit communities in Rhode Island include South Kingstown, Narragansett, Westerly, Jamestown, Charlestown and North Kingstown," National Grid said in a news release.

The utility said it estimates to have power restored to all affected customers by mid-week.