"We reject repeated subsidies and partial nationalization of European airlines, regardless of whether they are bought by European countries or state-run firms outside of Europe," Lufthansa said in a statement.
"We call upon the EU Commission to ban such side-stepping tactics," the statement said in a reference to European anti-trust and fair competition regulations.
Lufthansa did not explicitly name Etihad or Alitalia, but the statement was issued a day after the Abu Dhabi-based group said it had entered the final stage of an assessment of whether to purchase a stake in the troubled Italian carrier.
Etihad is the national airline of the United Arab Emirates and is expanding rapidly. It has bought minority stakes in several smaller carriers around the world as it competes with larger Gulf rivals Emirates and Qatar Airways.
Etihad owns 29 percent of Air Berlin, 40 percent of Air Seychelles, 19.9 percent of Virgin Australia and three percent of Aer Lingus.
Lufthansa said that outside Europe "there are highly integrated, national air traffic systems comprising airports, airlines and other service suppliers. These are expanding aggressively."
Europe would be able to compete with these only "if policymakers ensure that there is fair competition worldwide," Lufthansa argued.