Escalating his debate with civil liberties advocates, Mayor Rudolph W. Giuliani said yesterday that he had ''no problem'' with the DNA testing and fingerprinting of all newborns, although he did not propose actually gathering such records.

The Police Commissioner, Howard Safir, is already drawing both criticism and support for his new proposal that the police take DNA samples from the hundreds of thousands of people arrested every year in the city.

Mr. Giuliani, who backs the police plan, broadened the debate in a speech and news conference yesterday by endorsing the use of DNA tests in intensified city efforts to identify ''deadbeat'' fathers and force them to support their offspring financially. Children in single-parent homes are eight times more likely to commit crimes than those in intact families, he said.

Asked whether the DNA samples from children in support cases should also be given to law enforcement agencies, the Mayor said: ''The same way fingerprints are available, DNA should be available.'' He called DNA tests ''a wonderful protection for the innocent and another method of catching the guilty,'' as well as a tool for determining paternity.