Mateusz Morawiecki made the claim in Budapest as he attended a summit of the regional Visegrad Group (V4), which also includes Hungary, the Czech Republic and Slovakia, Poland's PAP news agency reported.
At a joint news conference with fellow heads of government from the three countries, Morawiecki said that "the level of solidarity and positive response to our concerns" expressed at the summit in Budapest had been "uplifting and unprecedented."
"Our coordinated diplomatic offensive is already bringing results," he added.
Morawiecki told reporters that talks had been held with international politicians including Iraqi Prime Minister Mustafa al-Kadhimi as well as leaders from Iraq's autonomous Kurdistan Region, Turkey and several Middle Eastern nations. In addition, efforts have been made to ensure "solid, policy-oriented cooperation" with countries such as Uzbekistan, he said.
"As a consequence, the influx of migrants into Belarus is currently much smaller than at its height two, three or four weeks ago," the Polish prime minister stated.
"And this is important because it's the first step towards defusing the crisis created by Belarus," he added.
Morawiecki told the news conference that the border crisis was "fundamentally political in nature," with Belarus's strongman leader Alexander Lukashenko teaming up with people smugglers and organised criminals to "pressurise and destabilise" the EU.
Poland's Border Guard said on Tuesday it had recorded 174 illegal attempts to cross from Belarus over the past 24 hours.
Since the start of the year, more than 36,000 such attempts have been recorded, including close to 7,000 this month alone, the agency's data showed.
Since September 2, Poland has kept the border zone under a state of emergency amid continuing migrant pressure. It is also set to build a 5.5-metre-high, 180-kilometre-long protective wall along the frontier.
The months-long migrant crisis on the Polish-Belarusian border has escalated in recent weeks, with Poland, the European Union and its member states, as well as NATO and the United States accusing Lukashenko of orchestrating the standoff in retaliation for Western sanctions against his regime.
Source: IAR, PAP, TVP Info