In an interview with the state-run TVP Info news channel, Wawrzyk said the sanctions became a realistic prospect thanks to Warsaw's diplomatic efforts, public broadcaster Polish Radio's IAR news agency reported.
"Crucially, this diplomatic offensive has resulted in what had previously seemed impossible, namely the United States working with the European Union," the diplomat noted.
"This demonstrates that both the Belarusian and Russian regimes are isolated internationally," he stressed.
Wawrzyk also called on Poland's opposition parties to resist Minsk's "hybrid war tactics" of "sowing division in Polish society."
If Polish parties are not divided on how to guard the eastern border, he said, "then this will exert a very sobering influence on both these regimes," the deputy foreign minister emphasised, as quoted by IAR.
Wawrzyk's remarks come after US President Joe Biden on Friday said that the situation on the border between Poland and Belarus was "of great concern," the state PAP news agency reported.
On Wednesday, Biden had discussed the issue with the head of the European Commission (the EU's executive arm), Ursula von der Leyen. On the same day, von der Leyen said that the bloc would agree on new sanctions against Belarus next week, according to IAR.
The measures will target regime officials as well as companies, the EC president added, with the matter set to be discussed by the EU's foreign ministers on Monday, IAR reported.
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 false promise of easy entry to the EU, and then leaving them at the bloc'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.
On Saturday, Poland's Border Guard agency tweeted that during the night, Belarusian soldiers had started to tear apart the temporary border fence, as a group of some hundred migrants attempted to illegally cross the frontier, PAP reported.
"Belarusian soldiers provided the foreigners with tear gas, which was used in the direction of the Polish forces," the agency also said, quoted by PAP.
"This and subsequent illegal attempts to cross the border were thwarted," Polish border officials added.
Polish police announced that on Friday, the body of a young Syrian man was found in a wooded area near the border with Belarus, outside the village of Wolka Terechowska, news agencies reported. The cause of death could not be determined at the scene, a police spokesman was quoted as saying.
Meanwhile on Saturday, Poland's Ministry of Defence said that a growing number of armed Belarusian functionaries was being deployed on the Belarusian side, near a migrant camp situated in front of the Polish village of Kuźnica Białostocka, IAR reported.
Source: PAP, IAR