The two politicians arrived in the northeastern city of Olsztyn to meet with border guards, police officers and soldiers jointly protecting the Poland-Belarus frontier, news agencies reported.
Duda said afterwards they discussed how the migrant crisis could develop and how to be prepared for every scenario.
The president told reporters that the border forces "are responding to a hybrid attack on the Polish border, and the external border of the European Union, in an exceptionally professional, responsible and brave manner."
"I thank you wholeheartedly for your valour, and I would like to assure all of our soldiers, border guards, police officers and their loved ones that we will do everything we can ... to make sure your service takes place in the most efficient, safest and best possible conditions," he said, as quoted by the state PAP news agency.
Błaszczak told reporters that the security of the frontier was being overseen by the Border Guard agency, with notable support from the army and police.
"The soldiers of the Polish army are highly skilled and excellently trained; they are professionals who take care of security," he said.
He added that the meeting also discussed the approaching winter and how to prepare for the harsher weather conditions.
"We are working to ensure the best possible conditions of service for our border forces," Błaszczak stated, as quoted by PAP.
The migrant crisis has been mounting since the summer, with Poland, the Baltics, the European Union, NATO, the United States and other Western nations all accusing Belarusian 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 the 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.
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 and late on Thursday, government officials said, as the border crisis escalated.
EU, NATO, US, UN nations condemn Belarus
The United States and European members of the UN Security Council on Thursday condemned Belarus for the “orchestrated instrumentalization" of migrants as tensions rose along the Polish-Belarusian border.
Earlier this week, the United States voiced concern over "disturbing images and reports" from the Polish-Belarusian border, and condemned Belarus for "orchestrating" migrants flows to Europe.
NATO has 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.