The attempt took place on Thursday evening near the frontier village of Kuźnica in Poland's eastern Podlaskie province, the Polish state news agency reported.
"The Belarusian army tried to push a group of some 35 people, mainly women and children, through to the Polish side," a spokesman for Polish police in the region said.
He added that the migrants had been "pushed onto the barbed-wire fence by Belarusian soldiers and the attempt was thwarted by Polish police officers, border guards and soldiers."
Currently some 200 people are camped nearby under Belarusian escort, the spokesman said.
Meanwhile, another 100 people are gathered on the Belarusian side, near the Polish village of Połowce, he added.
"These people haven't tried to cross the border as dozens of police officers, border guards and soldiers took position on the Polish side," the police spokesman also said, as quoted by PAP.
The migrant crisis has been mounting since the summer, with Poland, the Baltic states, the European Union, NATO and the US accusing Belarus President Alexander Lukashenko of orchestrating the standoff in revenge for sanctions imposed on his regime.
Minsk is deliberately luring vulnerable people, mostly Kurds from the Middle East, with the hope of safe passage to the West, and then leaving them at EU's doorstep, mainly on Poland's eastern border, officials have said.
On Wednesday, Polish Prime Minister Mateusz Morawiecki said the crisis was "designed to destabilise" the European bloc. He made the comment after talks in Warsaw with Charles Michel, who chairs the European Council of EU leaders.
Michel voiced solidarity with Poland, vowing that firm action would follow in the face of Belarus's "hybrid, brutal, violent and shameful attack," PAP reported.
Morawiecki told lawmakers on Tuesday that the migrant crisis was the most serious security risk facing Poland in decades, the news agency said.
Polish border guards, police and soldiers on Monday thwarted several bids by migrants to force their way into the country via Belarus, with fresh attempts taking place early on Wednesday, government officials said, as the border crisis escalated.
EU, NATO, US condemn Belarus
The United States on Monday voiced concern over "disturbing images and reports" from the Polish-Belarusian border, and condemned Belarus for "orchestrating" migrants flows to Europe.
NATO condemned the use of migrants by Belarus "as a hybrid tactic," with its Secretary-General Jens Stoltenberg voicing solidarity with Poland amid the border standoff.
Meanwhile, European Commission head Ursula von der Leyen called for EU member states to approve new sanctions against Belarus, which she said was responsible for a "hybrid attack" on the Polish border using migrants.
The European Union has accused Belarus of encouraging thousands of migrants from the Middle East and Africa to cross into EU countries via Belarus, as a form of hybrid warfare in revenge for Western sanctions on Minsk over human rights abuses, the Reuters news agency reported.
Poland and the Baltic states have accused Belarus's strongman leader Alexander Lukashenko of organising a wave of illegal migrants seeking to enter the bloc as part of what officials have called a "hybrid war."
The EU Commissioner for Home Affairs, Ylva Johansson, visited Poland in late September, agreeing with Warsaw’s arguments that “firm steps” were needed against Belarus, according to officials.
Poland's Morawiecki said last month that his country enjoyed full support within the European Union as it worked to defend itself against a migrant influx and a "hybrid war" being waged by Belarus.
In late September, Polish lawmakers voted overwhelmingly to extend a state of emergency in parts of two regions along the country's eastern border with Belarus by two months amid a growing migrant surge.
The state of emergency gives authorities broader powers to monitor and control the movement of people on the Polish-Belarusian border, which is also the eastern border of the European Union.