The evening rush-hour derailment between Bridgeport and South Norwalk caused about 70 injuries and tore up the tracks, which Finch said would need extensive repairs that would greatly complicate transportation into the New York area.
"We're in a pretty precarious situation here," Finch said.
CNN said the impact of the crash was compounded by major construction on the only other commuter rail line serving Connecticut and New York.
Many of the injured were treated and released, but about five people were admitted to hospitals with serious injuries, the Hartford (Conn.) Courant said Saturday.
The National Transportation Safety Board dispatched a team of investigators to Connecticut Saturday to look into the cause of the derailment, which Gov. Dannel Malloy said appeared to be an accident rather than an act of sabotage.
The two trains derailed after slamming together side-by-side. Witnesses told the Courant they felt a sharp bump and saw a cloud of smoke and dust as the trains jumped the tracks. While being evacuated, they saw a number of injured passengers being helped from other cars that had been heavily damaged.
Amtrak said Saturday service will remain suspended at least through Sunday between New York and New Haven, and there is no estimate on when it will be restored.