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The Obama campaign on Wednesday quickly seized on abortion and rape comments made by the Indiana Republican Senate candidate in an attempt to entangle the Republican presidential candidate, Mitt Romney, in a politically charged issue threatening to brew into a firestorm like the one that followed comments by Representative Todd Akin.

In a Senate debate Tuesday night, Richard Mourdock, the Indiana state treasurer, tried to distinguish himself from two opponents who also oppose abortion, explaining why he does not accept an exception for pregnancies conceived by rape.

“I’ve struggled with it myself for a long time, but I came to realize that life is that gift from God,” Mr. Mourdock said. “And even when life begins in that horrible situation of rape, that it is something that God intended to happen.”

On Wednesday morning, continuing to press a Democratic narrative that depicts the Republican Party as out of step with women, the Obama campaign sharply criticized the remarks.

President Obama “felt those comments were outrageous and demeaning to women,” Jen Psaki, the president’s campaign spokeswoman, told reporters Wednesday morning. “It is clear that Mitt Romney, that many Republicans who are running for office including him, including Mr. Mourdock, have very extreme positions on issues that women care deeply about,” she said, warning that women should be concerned if Republicans win both the White House and Senate.

Mr. Mourdock’s statements could singe Mr. Romney, who cut a television advertisement, released on Monday, endorsing Mr. Mourdock.

During her briefing with reporters, Ms. Psaki called it “perplexing” that Mr. Romney had not demanded that his endorsement ad be taken down from Indiana television. Mr. Romney supports abortion in the case of rape, incest and when the health of the mother is at risk.

The Democratic National Committee has tried to draw attention to the endorsement with a new video featuring a montage of debate footage.

Republicans had already tried to contain the fallout, strongly pushing back on the suggestion that Mr. Mourdock condoned rape.

Senator John Cornyn of Texas, the chairman of the National Republican Senatorial Committee, claimed that Mr. Mourdock’s position was no different from that of Representative Joe Donnelly, the Democratic candidate in the unexpectedly tight contest.

“Richard and I, along with millions of Americans — including even Joe Donnelly — believe that life is a gift from God. To try and construe his words as anything other than a restatement of that belief is irresponsible and ridiculous,” Mr. Cornyn said in a statement. “In fact, rather than condemning him for his position, as some in his party have when it’s come to Republicans, I commend Congressman Donnelly for his support of life.”

But the rape-and-abortion theme is threatening to push the close Indiana Senate race into the realm of the Missouri Senate race, another campaign that was supposed to favor Republicans before the Republican candidate, Todd Akin, defended his opposition to abortion in cases of rape and threw the contest off kilter. The incumbent Democrat in Missouri, Senator Claire McCaskill, is now expected to hold her seat.

During the Indiana debate, Mr. Mourdock’s comment did not yield much of a response from Mr. Donnelly, but other Democrats pounced. And Mr. Mourdock released a statement to clarify, “God creates life, and that was my point. God does not want rape, and by no means was I suggesting that he does. Rape is a horrible thing, and for anyone to twist my words otherwise is absurd and sick.”

Republicans noted that Mr. Donnelly, an Irish Catholic whose base is in South Bend, the home to University of Notre Dame, co-sponsored controversial legislation in 2011 that would have changed the federal ban on abortion funding to exempt conceptions from “forcible” rape, not just rape. The Mourdock campaign said this backing showed Mr. Donnelly believes pregnancies from statutory rape or incest should have to be carried to term.

Mr. Donnelly had said, earlier this year, that he was not aware that Republican authors of the bill had added the “forcible” language and was glad when an outcry forced them to remove it.

Mr. Cornyn tried Wednesday to change the subject.

“This election is about big ideas and the reality that our country is going in the wrong direction,” he said in a statement. “If you support Obamacare, government bailouts, reckless spending and higher taxes than you should vote for Joe Donnelly. But if you believe, as I do, that our government is too big, our taxes are too high, and we are passing an irresponsible debt onto future generations, than Richard Mourdock is your candidate to help get our country back on track.”

Mr. Mourdock beat Senator Richard Lugar, a six-term moderate, in the Republican primary in May.