"Solutions not taking into account the given country's abilities may prove completely counterproductive. That is why we are against any automatic quotas, but we are willing to talk about the scale of our engagement on voluntary terms," she said.
"Poland does not shun responsibility, our decisions have to be first of all effective in bringing help to those who need it, (but not for those) who see chances for better life (migrating to Europe)," she added.
Poland has agreed to take in 2,200 refugees and Kopacz said on Monday it could consider taking more. Germany and Austria are reportedly attempting to exert pressure on other member states to increase the numbers they are willing to take in, with some CEE states led by Hungary resisting the calls.
European Council President Donald Tusk warned on Thursday that divisions between western member states and their newer eastern partners were complicating efforts to solve the deepening migrant crisis.
"There is a divide ... between the east and the west of the EU. Some member states are thinking about containing the wave of migration, symbolised by the Hungarian (border) fence," Tusk said.
"Others want solidarity in advocating a so-called obligatory basis for quotas. The key challenge is to find for them all a common, yet ambitious, denominator," he said before talks with Hungarian Prime Minister Viktor Orban.
Tusk told a conference of EU ambassadors that the migrant crisis was one of the major challenges facing the 28-nation bloc.
"I am working with leaders to build a new consensus among governments on the EU response," he said.
"The first goal is to ensure people in need of international protection receive it. Second, we must gain more control of mass population flows."
Tusk said EU member states must take in at least 100,000 migrants. In May, the European Commission called on EU member states to take in 40,000 asylum seekers who had landed in Italy and Greece and a further 20,000 refugees who had not yet arrived in Europe.
"A fair distribution of at least 100,000 refugees among the EU states is what, in fact, we need today," Tusk said at a joint press conference with Hungarian Prime Minister Viktor Orban.
According to the EU external border protection agency Frontex, the total number of refugees detected at the bloc's borders between January and July 2015 stands at over 340,000, which is three times higher than during the same period of the previous year. Many of the migrants enter the European Union through the Balkan Peninsula. (jh/rk)