His comments came as other Republicans in recent days have questioned or challenged birthright citizenship, embracing a cause that had largely been confined to the far right.
The senators include Arizona's John McCain, the party's 2008 presidential nominee; Arizona's Jon Kyl, the Republicans' second-ranking senator; Alabama's Jeff Sessions, the top Republican on the Judiciary Committee, and Lindsey Graham of South Carolina, a leading negotiator on immigration legislation.
"I'm not sure exactly what the drafters of the (14th) amendment had in mind, but I doubt it was that somebody could fly in from Brazil and have a child and fly back home with that child, and that child is forever an American citizen," Sessions said.
Legal experts say repealing the citizenship right can be done only through constitutional amendment, which would require approval by two-thirds majorities in both chambers of Congress and by three-fourths of the states. Legislation to amend the right, introduced previously in the House, has stalled.
The proposals are sure to appeal to conservative voters as immigration so far is playing a central role in November's elections. They also could carry risks by alienating Hispanic voters and alarming moderates who could view constitutional challenges as extreme. Hispanics have become the largest minority group in the United States, and many are highly driven by the illegal immigrant debate.
McConnell and McCain seemed to recognize the risk by offering guarded statements Tuesday.
McCain, who faces a challenge from the right in his re-election bid, said he supports reviewing citizenship rights. He emphasized, however, that amending the Constitution is a serious matter.
"I believe that the Constitution is a strong, complete and carefully crafted document that has successfully governed our nation for centuries and any proposal to amend the Constitution should receive extensive and thoughtful consideration," he said.
At a news conference, McConnell refused to endorse Graham's suggestion that citizenship rights be repealed for children of illegal immigrants. While refusing to take questions, he suggested instead that he would look narrowly into reports of businesses that help immigrants arrange to have babies in the United States in order to win their children U.S. citizenship.
The 14th Amendment, adopted in 1868 in the aftermath of the Civil War, granted citizenship to "all persons born or naturalized in the United States," including recently freed slaves.
Defenders of the amendment say altering it would weaken a fundamental American value while doing little to deter illegal immigration. They also say it would create bureaucratic hardships for parents giving birth.
Quoting a newspaper columnist, Senate Democratic leader Harry Reid of Nevada said Republicans were "either taking leave of their senses or their principles" in advocating repeal.
An estimated 10.8 million illegal immigrants were living in the U.S. as of January 2009, according to the Homeland Security Department. The Pew Hispanic Center estimates that as of 2008, there were 3.8 million illegal immigrants in this country whose children are U.S. citizens.