US Secretary of Defence Robert Gates has urged Germany to send more troops to Afghanistan.
There are concerns that the mission may be failing
He warned that without reinforcements the Nato-led force could lose credibility in the country.
A German newspaper described Mr Gates' letter to German Defence Minister Franz Josef Jung as "unusually stern", and its response equally blunt.
Correspondents say the exchange comes amid growing signs of strain in the mission and in Nato as a whole.
Canada's Prime Minister Stephen Harper has issued both US President George W Bush and UK Prime Minister Gordon Brown with an ultimatum - that Canada will end its military mission in Afghanistan if Nato does not put more soldiers in the dangerous south of the country.
Mr Gates's appeal comes amid strains in the Nato alliance
The newspaper Sueddeutsche Zeitung said it was sent about 10 days ago.
It asks for Germany to consider a new mandate which could allow thousands more troops to be sent to Afghanistan with some deployed to the more dangerous south.
The Nato-led force has almost 37,000 troops in Afghanistan.
Germany currently has 3,200 troops stationed in northern Afghanistan and around the capital, Kabul.
According to the current parliamentary mandate, the troops can only be sent elsewhere under exceptional circumstances.
The letter complains of a heavy burden on US troops and of a possible split in the Nato alliance.
The US has already promised to send an extra 3,000 US marines - but is urging other Nato countries including France and Germany to do more.
So far most Nato members have refused to send significant numbers to southern Afghanistan.
HAVE YOUR SAY
Germany is a part of Nato and is obliged to send in more troops
Rob, Wirral, UK
In a meeting with Mr Gates in Washington on Thursday, French Defence Minister Herve Morin called for a "comprehensive strategy" in Afghanistan but failed to pledge any more combat troops.
The BBC's Jonathan Beale in Washington says the US has tried to avoid a public row with Nato members.
But speaking to a senate committee a senior US diplomat stated that "we expect more from our Nato allies", adding that too few allies had combat troops fighting the insurgents in the south.
LEAD INTERNATIONAL FORCES IN AFGHANISTAN
Locations refer to International Security Assistance Force (ISAF)
Total contributing nations: 39
ISAF total strength: Approx 41,700