The rail company said its stance was due to "railway transport" security reasons.
Police shut down the Keleti terminal to migrants on Tuesday, preventing those with valid tickets but no travel documents from boarding trains to Austria and Germany, many migrants' preferred destination.
There was no immediate explanation from police or other authorities of today's decisions, which came hours before Hungarian Prime Minister Viktor Orban was to meet European Union leaders in Brussels to discuss the crisis.
Hungary tantalizingly opened the way Monday, allowing more than 1,000 migrants to pack westbound trains and inspiring a migrant surge to the capital before it withdrew the option 24 hours later.
Hungary, which for months had permitted most applicants to head west after short bureaucratic delays, now says it won't let more groups deeper into the European Union and claims EU backing for the move.
With an estimated 3,000 people camping outside the station, conditions have grown increasingly squalid despite the efforts of volunteers distributing water, food, medicine and disinfectants.
