On Thursday, police let the migrants board the train in Budapest but then tried to force them off at a refugee camp to the west of the capital.
Hungarian MPs face a key vote later on whether to tighten border controls as migrants try to pass through to their preferred destination, Germany.
Three other European meetings on Friday will discuss the migrant crisis.
Members of the European Commission are also flying to the Greek island of Kos to examine the difficulties caused by the large numbers of refugees and migrants landing there.
Live updates on the crisis
Tour of migrant camp in Budapest station
Meanwhile, a Syrian Kurdish child who drowned while attempting to cross to Kos is due to be buried in his hometown of Kobane on Friday.
The family of Alan Kurdi crossed the border from Turkey to Syria, carrying coffins bearing his body and those of family members who died with him.
Images of the toddler's limp body, washed ashore on a Turkish beach, were widely circulated on Thursday, heightening outrage over the migrant crisis.
The Hungarian MPs will also vote on creating new holding camps for migrants, and on whether the situation constitutes a state of emergency.
Prime Minister Viktor Orban on Thursday described the situation as a "German problem" as Germany was where those arriving in the EU "would like to go".
However, Luxembourg's Foreign Minister Jean Asselborn - who is heading the EU meetings on the crisis - criticised Hungary's conservative leader on German television on Thursday night, saying: "One sometimes has to be ashamed for Viktor Orban."
European Council President Donald Tusk said at least 100,000 refugees should be distributed across EU states - a sharp increase on a previous European Commission target of 40,000.
German Chancellor Angela Merkel and French President Francois Hollande said they would present plans for the redistribution of refugees within the EU.
