Mr Schulz has claimed that “too many questions are still open,” as he appeared live on Germany’s ZDF channel.
Schulz and the SPD are lagging behind Ms Merkel and the Christian Democrats (CDU) in polls with just two weeks left until the September 24 election.
The first debate, held on September 3, saw Mr Schulz fail to make any ground on his main rival as he turned in a poor performance.
A poll held after the debate showed viewers found Merkel’s performance to be more convincing with 55 per cent saying she was the stronger candidate, while just 35 per cent saw Schulz as superior.
A Twitter survey carried out by Insa had the SDP trailing with 23.5 per cent behind the CDU who held a commanding 36.5 per cent of the votes.
The SDP leader made the request to the Chancellor while he answered questions from the studio audience.
The 21-year-old nurse Alexander Jorde, from Hildesheim in northern Germany, confronted the Chancellor after reading the CDU party manifesto’s claim that no one has to worry about care in the country.
Mr Jorde claimed the dignity of people in nursing homes and hospitals had been “violated a thousand times”.
Speaking during the TV programme Mr Jorde said: “The nursing profession is in itself a beautiful profession – it is not just about a***-wiping.”
Ms Merkel was forced to admit that she would seek to close the health system’s skills gap by hiring nurses from other EU countries.
She also urged industry members to use salary negotiations to demand higher wages.
The German Chancellor said: “I can not promise that in the end everything will be to your satisfaction, but there will be better standards. I hope it will be better in two years.”