Estonia has accused Russia of deliberately directing would-be migrants to its border.
The claim was made after Finland confirmed it was sealing all but one crossing point with Russia.
Finland claimed Russian guards were encouraging people originally from countries including Yemen, Afghanistan, Somalia and Syria, to try to cross.
The Kremlin has denied the allegations made by Finland, but has yet to comment on the claims from Estonia.
Last week, Finland's prime minister announced four border crossings in the south were being closed.
Petteri Orpo accused Russia of deliberately helping people without proper documentation to get to the border.
Mr Orpo said on Wednesday that Finland was now closing all but the northernmost Raja-Jooseppi crossing from midnight local time.
Finland shares a 1,340km (833 mile) border with Russia.
According to Reuters news agency, Finnish officials said on Wednesday that Russian were likely to be directly involved in more than 600 asylum-seekers arriving there over the past two weeks.
Estonia's public broadcaster ERR reported that 75 migrants had tried to enter Estonia from Russia through the Narva crossing point since Thursday last week. None had asked for asylum and all were turned back.
A spokesperson for interior minister Lauri Laanemets told Reuters that Estonia had made preparations to close border crossings if "the migration pressure from Russia escalates."
They said migrants were appearing at the Estonian border in small groups "in an orchestrated manner."
