Germany has complained to Greece and the EU about the treatment of migrants on the Greek-Turkish land border.
The German government says it has called for "substantial improvements" in the Greek detention centres where migrants are being held.
The EU border police agency Frontex has also asked Athens to investigate reports that force was used to prevent illegal migrants entering Greece.
A 175-strong Frontex team, including 26 Germans, is helping Greek police.
According to Frontex, large numbers of migrants in the area claim to be from Afghanistan, followed by others claiming to be Palestinians - though many turn out to be from Algeria. Others claim to be from Pakistan or Iraq.
All those found to have crossed the border illegally are detained. This year it has become the EU's main migration hotspot.
The UN refugee agency UNHCR has criticised overcrowding and poor hygiene in the Greek detention centres, where unaccompanied children are among those held.
Human rights groups have also accused Greece of deporting some migrants to Turkey before proper screening of asylum claims.
Plea for clear rules
Frontex began its deployment in early November, in the Orestiada area of north-eastern Greece. The mission, initially due to last up to two months, has now been extended until 3 March 2011.
Illegal border crossings in the area dropped by 44% in November, Frontex says.
A Frontex spokesman, Michal Parzyszek, told the BBC that Germany was continuing to participate fully in the mission, called Rabit 2010.
But he said German police had expressed their concerns to Frontex unofficially.
Earlier the German news website Spiegel said German police had been ordered to stop participating in some operations on the Greek-Turkish border.
Mr Parzyszek said "our goal now is to amend the operational plan - we want to make it very detailed, to avoid any confusion about what to do, when and how".
"We haven't received any answer from the Greek authorities yet," he added.
Frontex police are under orders to act in line with Greek rules and to act always in the presence of their Greek colleagues.
"[Frontex] officers can exercise powers exactly like the host country - and 95% of them carry weapons," Mr Parzyszek said.
In the second quarter of this year 90% of the migrants detected trying to enter the EU illegally were on the Greek land border, Frontex says.
The number of migrants crossing the Evros river into Orestiada has soared this year. The UNHCR says 38,992 arrived in the 10 months to November, compared with 7,574 for the same period of 2009.
The UNHCR says tighter border controls at sea, with Mediterranean countries co-ordinating their efforts, have simply shifted the problem of illegal migration to the Greek land border.
This year as many as 44 migrants bound for Greece have drowned in the Evros river, though the real figure is believed to be higher, the UNHCR said in mid-October.
"It's a real humanitarian crisis," UNHCR spokeswoman Ketty Kehayioylou told the BBC on Tuesday.
The migrants lack legal aid, including interpreters, so they have no chance to apply for asylum, she said.
Another UNHCR official, Stella Nanou, welcomed Greece's plan to reinstate an asylum appeals board. It means some of the backlog of 46,000 asylum applications may now be re-examined, she said, but "it's not clear when that will happen".
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