Police in Budapest lifted a two-day blockade of the Keleti station, allowing migrants to enter. But some inadvertently boarded trains bound for a refugee camp outside the capital.
Hungarian authorities stopped the migrants, including refugees from Syria and Iraq, from boarding trains bound for Western Europe. The station has become the latest flashpoint in the migrant crisis.
Prime Minister Viktor Orban has adopted staunchly anti-migrant positions to try and win back supporters from the far right, which is making significant gains.
Authorities had been allowing migrants to travel without checking passports, but on Tuesday, the station was closed and migrants began protesting.
Europe has seen an unprecedented number of migrants and asylum seekers reach its borders. EU ministers called the meeting, in part, to try to decide which migrants are treated as refugees.
The three Syrian children, aged 5 and 6, were near death from dehydration when they were discovered by police in the back of a minivan on Saturday.