"Of course the government will work closely and in the spirit of partnership with the new Greek government," said the spokesman, Steffen Seibert.
"This offer applies both to jointly overcoming the debt crisis, and to the challenges posed by the refugee situation, for which we need common answers."
Greece, which has suffered five years of economic crisis, in July signed a third loans-for-reforms deal with international creditors, saving it from a chaotic exit from the eurozone.
Seibert said on Greece's financial and economic woes that "we have a very clear basis for overcoming the debt crisis, and that is the agreements in the third aid package."
Also Read
He stressed that the deal was signed "not with some government, but with the Hellenic Republic... That means it remains valid in its entirety, beyond elections and changes of government."
"And on this basis, we and certainly the other European partners will cooperate with the new Greek government."
They also talked about an EU summit set for Wednesday to discuss the migrant crisis and "agreed to closely cooperate on the issues to be discussed there as well as on other bilateral and European issues," Seibert added.