Amtrak resumed service with a 5:30 a.m. southbound train leaving New York City. The first northbound train, scheduled to leave Philadelphia at 5:53 a.m., was delayed and pulled out of 30th Street Station at 6:07 a.m. Both trains arrived at their destinations about 30 minutes behind schedule.
About 60 people boarded the New York-bound train in Philadelphia, including two dozen reporters and photographers. Mayor Michael Nutter was on hand to see the train off and hugged the first passenger in line.
All Acela Express, Northeast Regional and other services also resumed.
Amtrak officials said Sunday that trains along the Northeast Corridor from Washington to Boston would return to service in "complete compliance" with federal safety orders.
In Philadelphia on Monday, Nutter stood on the platform, greeting passengers and crew members. He pulled out his cellphone and snapped pictures as the train rolled out.
"It's great to be back," said Christian Milton, of Philadelphia. "I've never had any real problems with Amtrak. I've been travelling it for over 10 years. There's one accident in 10 years. Something invariably is going to happen somewhere along the lines. I'm not worried about it."
Milton said he'd think about the victims and maybe say a prayer as the train navigated the curve where the derailment happened.
President Barack Obama, landing in Philadelphia before a visit to nearby Camden, New Jersey, thanked the city and its rescue workers for their response to the derailment.
He shook hands with Nutter, police Commissioner Charles Ramsey and other city officials after arriving at Philadelphia International Airport on Air Force One.
At New York City's Penn Station early Monday, police with dogs flanked the escalator as a smattering of passengers showed their tickets to a smiling Amtrak agent and headed down to the platform.
A sign outside the train flashed "All Aboard" in red letters.
The conductor gave a broad all-clear wave, stepped inside and the Philadelphia-bound train glided out of the station.
Passenger Raphael Kelly, of New York, looking relaxed, said he was "feeling fine" and had "no worries."
Kelly, who takes Amtrak to Philadelphia weekly, said with a smile that if he did have any concerns, "I have to get over it."
Tom Carberry, who had been driving 45 minutes to an hour to take a commuter train from Trenton, New Jersey to New York, praised Amtrak for restoring service so swiftly.
"My biggest takeaway was the under-promise and over-deliver, and the surprise of having it come back this morning when that wasn't expected," said Carberry, of Philadelphia. "That was a good thing for Amtrak."
Amtrak spokesman Craig Schultz said it was important to restore service, calling the Northeast Corridor "an economic engine here on the East Coast."
Almost 20 people injured in the train crash remain in hospitals, five in critical condition. All are expected to survive.
Lawyers for four passengers announced lawsuits against Amtrak on Monday.
They include two cousins from Spain — one of whom nearly lost an arm — and a Brooklyn advertising executive who broke ribs, tore knee ligaments and lost teeth but staggered to help people before collapsing and being carried away on a gurney, lawyers said.
Sen. Bill Nelson, D-Fla., introduced legislation Monday that would increase the cap on damages Amtrak could be forced to pay from lawsuits from $200 million to $500 million.
Amtrak has said it does not comment on lawsuits.
Investigators with the National Transportation Safety Board have focused on the acceleration of the train as it approached the curve, finally reaching 106 mph as it entered a 50 mph stretch and managing to slow down only slightly before the crash.
The Amtrak engineer, among those injured in the crash, has told authorities he doesn't recall anything in the few minutes before it happened. Characterizing engineer Brandon Bostian as extremely safety conscious, a close friend said he believed reports of something striking the windshield were proof the crash was "not his fault."
"He's the one you'd want to be your engineer. There's none safer," James Weir of Burlison, Tennessee, told The Associated Press in a telephone interview Sunday.
Investigators also have been looking into reports that the train's windshield may have been struck by some sort of object, but NTSB member Robert Sumwalt said on CBS's "Face the Nation" program Sunday that he wanted to "downplay" the idea that damage to the windshield might have come from someone firing a shot at the train.
"I've seen the fracture pattern; it looks like something about the size of a grapefruit, if you will, and it did not even penetrate the entire windshield," Sumwalt said.
Officials said an assistant conductor on the derailed train reported hearing the Amtrak engineer talking with a regional train engineer, and both said their trains had been hit by objects. But Sumwalt said the regional train engineer recalls no such conversation, and investigators had listened to the dispatch tape and heard no communications from the Amtrak engineer to the dispatch centre to say that something had struck the train.
Associated Press writers Kiley Armstrong in New York City and Shawn Marsh in Trenton, New Jersey, contributed to this report.