After years of delays and safety and design disputes, Amtrak is one step closer to bringing new high-speed trains to the busy Northeast Corridor.

Amtrak officials said late Friday that the new trains, which had failed an extended series of computer modeling tests, had passed on the 14th try and had been cleared by the Federal Railroad Administration to begin testing on the tracks that run from Washington, D.C., to Boston.

The faster, more spacious trains — sets of locomotives plus passenger cars — come with a price tag of about $1.6 billion and are to replace those in the Acela fleet, which should have been decommissioned at the end of their life cycle in 2016.

The sleek new red, white and blue Avelia Liberty trains are to travel at a max speed of about 160 miles per hour because of a limit imposed by the northeast corridor’s aging tracks, 10 miles faster than the current Acela trains, and are expected to tilt for a faster and smoother ride around curves. They accommodate up to 386 passengers, an increase of 25 percent.

The testing on the tracks will be “the next step in the safety certification process that leads toward launching revenue service,” Amtrak said in a statement.

Cliff Cole, a spokesman for Alstom, the French manufacturer of the new trains, hailed the move to on-track testing as progress for passengers “who will soon discover a brand-new travel experience on the busiest rail corridor in America.”