Germany, a favoured destination for refugees fleeing war in the Middle East, expects a record 800,000 to 1 million asylum seekers to arrive this year.
The influx is proving a major logistical challenge, straining resources as the authorities struggle to register and house all the new arrivals, some of whom remain in tents as winter approaches.
Merkel has seen her popularity ratings slump to a four-year low and some members of her Christian Democrats (CDU) and their Bavarian sister party, the Christian Social Union (CSU), want her to take a tougher line with comprehensive border controls.
"We mustn't raise the white flag," CDU lawmaker Clemens Binninger said.
The conservatives' parliamentary leadership estimates around a fifth of their lawmakers hold similar views on toughening policy towards refugees.
But participants at Tuesday's meeting of the conservatives' parliamentary group said Merkel rejected calls from some of the lawmakers for refugees arriving from Austria to be turned away.
If Germany took such a course, it would have disastrous consequences for all countries on the asylum seekers' route from the Balkans as Austria and Hungary would then have to turn away refugees as well, the participants said Merkel had told the meeting.
Instead, Merkel said she would seek during planned talks in Turkey this weekend greater cooperation with Ankara to stem migration flows, though could give no promises on how quickly that could be achieved.
The conservative lawmakers unanimously supported a draft bill drawn up by the CDU-run Interior Ministry that provides for transit zones to hold refugees at border crossings so asylum requests can be examined before they are allowed in.
Sigmar Gabriel, vice chancellor and leader of the Social Democrats (SPD), junior partner in Merkel's ruling coalition, criticised the idea of transit zones.
Participants at an SPD meeting said he dubbed them "detention zones".
