(CNN) Rand Paul says he doesn't want to be grilled about abortion until Democratic National Committee Chairwoman Debbie Wasserman Schultz answers similarly tough questions.

Wasserman Schultz hit back -- highlighting Paul's testy interviews with female television anchors , too, by saying she hopes he can "respond without 'shushing' me." But Paul, the Kentucky Republican senator who launched his 2016 presidential campaign this week, said her answer made it sound like she is indeed okay "killing a seven-pound baby."

Paul, the Kentucky Republican senator who launched his 2016 presidential campaign this week, bristled at a question about abortion while talking with reporters in New Hampshire on Wednesday.

"Why don't you ask the DNC, 'Is it OK to kill a seven-pound baby in the uterus?'" Paul said.

His comment came after The Associated Press published a report that said Paul had ducked questions about his views on what exceptions -- if any -- he'd support if abortion were to be banned.

In a press conference shortly after the AP's story was published, Paul said discussions of abortion focus too much on "exact details" on the right, and that Democrats should face similarly complex questions.

"We always seem to have the debate way over here on what are the exact details on exceptions or when it starts," Paul said.

He said reporters should go to Wasserman Schultz with similar questions -- and then ask him again.

"You go back and you ask Debbie Wasserman Schultz if she's okay with killing a seven-pound baby that is just not yet born yet. Ask her when life begins, and you ask Debbie when she's willing to protect life," he said. "When you get an answer from Debbie, come back to me."

Wasserman Schultz quickly responded, saying Paul should explain whether he believes abortion should ever be legal.

"Here's an answer," she said in an emailed statement. "I support letting women and their doctors make this decision without government getting involved. Period. End of story. Now your turn, Senator Paul."

Then, she posed some questions of her own, saying: "We know you want to allow government officials like yourself to make this decision for women -- but do you stand by your opposition to any exceptions, even when it comes to rape, incest, or life of the mother? Or do we just have different definitions of 'personal liberty'? And I'd appreciate it if you could respond without 'shushing' me."

But Paul wasn't fazed — or impressed — by Wasserman Schultz's answer. In an interview with CNN's Wolf Blitzer, the senator said it seemed to him like she wasn't opposed to late-term abortions.

"Sounds like her answer is yes, that she's okay with killing a seven-pound baby," he said.

Paul went on to say that "even most of my friends who are pro-choice" are opposed to such abortions, but acknowledged that "there's a bit of doubt and discussion [about abortions] earlier in the pregnancy."

"But Debbie's position, which I guess is the Democrat Party's position, that an abortion all the way up until the day of birth would be fine, I think most pro-choice people would be really uncomfortable with that," he added. "So I don't know -- I really think she's got some explaining to do."