FRANKFURT—Germany's Angela Merkel urged European Union countries that have refused to take on a share of the bloc's refugees to reconsider, as a new poll indicated that half of Germans don't want her to seek another term as chancellor.

"What I still say doesn't work is for some countries to say, 'We don't want to have Muslims at all, even if it's necessary for humanitarian reasons,'" Ms. Merkel said in an interview with German broadcaster ARD on Sunday.

The German chancellor just finished a week of meetings in which she met with more than a dozen leaders from across the EU. On Friday in Warsaw, she appeared alongside leaders from the Visegrad Four countries—Slovakia, the Czech Republic, Poland and Hungary—which have criticized her open-door policy for refugees. The group has repeatedly pushed back against calls for an EU-wide refugee distribution key to share the burden of new arrivals.

Meanwhile, pressure is growing on Ms. Merkel at home. In a survey published on Sunday, the Bild am Sonntag newspaper said 50% of the 501 people surveyed said they opposed a fresh term for her when the country goes to the polls in October 2017. In turn, 42% would like the chancellor to stand again next year.

The result marks a drop in support for Ms. Merkel since a similar survey last November, which found that 48% of Germans opposed a fourth term for the chancellor, while 45% were in favor. Her popularity has slumped in recent weeks amid mounting criticism of her refugee policy following a series of attacks in Germany, two by asylum seekers who had pledged allegiance to Islamic State.

The chancellor has yet to say whether she will seek another term. "At no time have I said when I want or don't want" to announce plans to run again, she said in Sunday's television interview. "Today I don't want to say anything more about this."

Within Ms. Merkel's ruling coalition, new calls for limiting the number of refugees entering Germany are also emerging. Vice Chancellor Sigmar Gabriel, the head of Ms. Merkel's center-left coalition partner, voiced support for a refugee cap for the first time on Sunday

"There's something called an upper limit," Mr. Gabriel said, speaking at an open-house event in Berlin hosted by the government. "That is the ability of our country to integrate" refugees.

Ms. Merkel stood firm on her migration policy, repeating a list of new policies that she has introduced to meet the challenges of the refugee crisis.

"We have made harder rules for those who have no potential to remain," Ms. Merkel said in the television interview. "We have also told refugees that we expect that they obey our laws, that you learn German, and we've created the possibility to punish" those who don't.

Despite the refusal of some EU countries to take in refugees, Ms. Merkel added that the bloc was able to operate effectively in a crisis.

"In Europe at the moment, in the last 12 months, we have done a lot," Ms. Merkel said. "Within five days we got a NATO mission up and running on the Aegean. In just a few months, we negotiated a deal between the EU and Turkey."

The bloc has been left soul-searching since June when the U.K. voted in a referendum to quit the EU. Ms. Merkel's meetings with European leaders in the past week were aimed at preparing an informal meeting next month of the remaining 27 member states bloc in the Slovakian capital of Bratislava, where leaders hope to present a unified front in the face of a British exit.

Write to Tom Fairless at tom.fairless@wsj.com

(END) Dow Jones Newswires

August 28, 2016 23:55 ET (03:55 GMT)