A group of activists made their way from the concourse at Manchester Piccadilly onto the tracks at about 1pm on today (Sunday).
It resulted in services being halted, affecting commuters in Yorkshire and across the country.
Superintendent Mark Cleland, from British Transport Police, said officers will use full investigative resources to track down offenders.
He said: "While we appreciate and respect the right to peaceful protest, when this compromises the safety of the public and the protesters themselves, any offenders will attract the full investigative resources of BTP.
"Those involved in this afternoon's incident will be subject to intense investigation with a view to arrest and prosecution.
"All protesters at Manchester Piccadilly have now been safely moved from the tracks and the station has reopened.
"We will continue to maintain a police presence at this station and at other stations across the rail network."
The action, which saw scores of flag-waving protesters make it on to the tracks, was thought to be in opposition to Turkey's war with Syrian Kurds.
Police gave the all-clear to reopen the station at about 6.30pm, but National Rail warned that normal service would not resume until after 8pm.