Obermann said the company is looking for additional cost savings to boost competitiveness, above the 4.7 billion euros it has targeted in cost cuts by 2010.
"If we see further potential, we will of course exploit it. We are certainly working hard at it," Rene Obermann said after the company announced 2007 earnings.
The German market, where Deutsche Telekom hopes to compensate losses at its traditional fixed-line unit with new DSL broadband connections, accounts for about half of its revenues.
The group has been at pains to keep domestic customers from switching to rivals such as Vodafone or smaller local phone and Internet service providers.
A decline in prices for mobile phone rates in Germany resulted in a 2.7 percent drop in revenue and an 11.1 percent decline in core profit at T-Mobile Germany, the company said.
Revenue growth abroad, however, remained at a high level.
Excluding Germany, it rose 12.2 percent to 27.1 billion euros as core profit abroad increased by 17.8 percent to 7.9 billion.
Deutsche Telekom said tax effects led to a 2007 net loss of 757 million euros, though adjusted net profit was 808 million.
Obermann also said the company was close to concluding talks on a partnership for the systems integration unit of its business client unit T-Systems.
"I am talking of days or weeks," Obermann said.
Deutsche Telekom has been searching for a partner for the unit for almost a year now.
-- Reuters contributed to this report