Steinbrück, the opposition Social Democrats' candidate, was hoping to use the debate to win over undecided voters, as opinion polls give Chancellor Merkel a significant advantage in terms of personal popularity.
The polls also indicate that Merkel's conservative Christian Democrats (CDU) and their junior coalition partners, the liberal Free Democrats (FDP) would likely win more votes than the Social Democrats (SPD) and their preferred coalition partners, the Greens.
However, it's not clear whether the pro-business FDP will clear the five-percent hurdle required to send its deputies back into the Bundestag parliament in Berlin.
12 million viewers
Putting the questions during the 90-minute debate were four talk-show interviewers drawn from Germany's public and private broadcasting stations. Some 12 million viewers were expected to watch the televised debate, the only one planned between the CDU and SPD candidates.
In his opening remarks, Steinbrück said, if elected, he would tackle societal gaps between rich and poor by introducing a standard minimum wage, ensure educational chances for all and equal pay for women alongside men.
Merkel said her coalition government's financial policies of the past four years had been "pretty sensational" in stabilizing the job market and promoting research and development.
"We had four good years in Germany," she said, referring to her coalition's current term.
On the issue of minimum wages, she said the setting of wage levels was the task of the employers and trade unions at collective bargaining, she said.
"We should not do anything that endangers jobs," she said, adding that tax rises planned by the SPD and Greens would worsen the situation.
Steinbrück replied that his Social Democrats wanted to ask the "upper five percent" of Germany's income-earners to contribute more to public coffers.
Questioned on Greece
On the issue of a further bailout tranche for troubled eurozone nation Greece, Merkel said a new aid package might be needed, but that nobody knew exactly "how things would develop in Greece."
Steinbrück said Europe could not just use what he called the "austerity stick." What was needed was a reconstruction program, he said.
A current initiative to tackle Europe's high level of youth unemployment had not gathered momentum, Steinbrück added.
Pre-kindergarten care in focus
The latter stages of the debate focused on Germany's increasingly elderly population and on care for the very young.
Merkel said her government had created additional places for children under the age of three via daycare providers. Steinbrück said a future SPD-led coalition would scrap a recently introduced childcare subsidy to parents and would instead invest in nursery schools or kindergartens. The subsidy was introduced in response to a new law that gives any parent the legal right to daycare for their children - because there are too few places around the country, Merkel's government argues that the subsidy serves to reduce public demand.
On Syria, both rule out go-it-alone strikes
Merkel said Germany would not participate in a possible military strike currently being discussed by the United States and France as punishment for last month's suspected chemical weapons attack in Damascus, Syria.
It was a "terrible crime," Merkel said.
"If at all, Germany could only participate under a United Nations mandate," she said. "A political process must come into motion."
A collective response in compliance with international law was needed, she said. At next week's G-20 economic summit in St Petersberg, Merkel said she intended to consult with the leaders of Russia and China on the crisis.
Steinbrück too said he could only consider a reaction based on a mandate that complied with international law. Referring to German NATO military personnel with Patriot missile units in Turkey and on board AWAC surveillance aircraft, Steinbrück said he would make sure that German soldiers were not involved in a unilateral military strike.
NSA, data privacy
Steinbrück said Merkel's coalition government had failed to clarify the alleged wire-tapping of private German electronic communications by US and British intelligence agencies.
Merkel said she had no grounds to mistrust assurances given by the United States and Britain.
ipj/pfd (dpa, AFPD)