Starkly different responses to the shootings in Newtown, Conn., from the governors of Virginia and Maryland on Tuesday serve as fresh reminders that one of the nation’s deepest divides on gun control runs along the Potomac River.

After 20 children and six adults were killed at Sandy Hook Elementary School last week, Virginia Gov. Robert F. McDonnell said Tuesday that the commonwealth should consider arming teachers, principals and other school staff members. Maryland Gov. Martin O’Malley took an opposite tack, saying that “too many guns” are in circulation already and that he may propose a statewide ban on assault weapons.

McDonnell (R) and O’Malley (D), the outgoing chairmen of their parties’ national governors groups, are used to deep-blue Maryland and purple Virginia differing on a host of issues. But the stakes are higher now as the shootings at Sandy Hook put pressure on elected officials to face the renewed debate over guns.

During the “Ask the Governor” radio show on WTOP on Tuesday, McDonnell was asked whether teachers and principals should be armed inside schools.

“I know there’s been a knee-jerk reaction against that,” McDonnell said. “I think there should at least be a discussion of that. If people were armed, not just a police officer but other school officials who were trained and chose to have a weapon, certainly there would have been an opportunity to stop aggressors coming into the schools.”

Early this year, Virginia lawmakers repealed a 19-year-old law that had limited handgun purchases to one per month. They also stripped localities of the right to require fingerprints from people applying for concealed-handgun permits. Carrying a concealed weapon with a permit is legal in the state, but not at schools.

“Right now we have a complete ban [at schools], and I’ve been supportive of that,” McDonnell said. “But I think that’s a discussion that is probably timely. Especially, you look at the facts . . . in Connecticut, where this person went into the principal’s office and actually killed the principal, who was lunging . . . at the perpetrator heroically to try to stop him. If a person like that was armed and trained, could they have stopped the carnage in the classroom? Perhaps.”

McDonnell did not completely dismiss the idea of restricting large ammunition clips like the kind police say Adam Lanza used in Newtown, but he said he thinks the problem is rooted in mental illness and a culture that does not value life.

Rep. Gerald E. Connolly (D-Va.) noted that some people similarly argued after the 2007 Virginia Tech massacre that the shootings could have been prevented if more guns were allowed on campus, drawing a sharp rebuke from some families of victims. “I think it’s an outrageous, extreme and reprehensible statement,” Connolly said of McDonnell’s comments.

In Annapolis, O’Malley questioned whether arming school officials is “the most prudent course.”

“It’s hard to imagine a level of weaponry that a security guard . . . would be carrying on their belt that could have resisted the sort of attack that that individual perpetrated in Newtown,” he said.

O’Malley said Tuesday that he is likely to propose legislation that could include a ban on assault rifles and other gun-control measures, as well as proposals for mental-health and school safety legislation.

“I think we have too many guns, and I think we have too much killing,” O’Malley told reporters at the statehouse, saying he and state lawmakers are asking “what more can we do.”

O’Malley stressed that his plans are “very much a work in progress,” adding that he senses a strong will among legislators to take action in the 90-day session that will start Jan. 9.

“I think there’s been a change of heart and a greater open-mindedness in the wake of the murder of the innocent in Connecticut for people to take a look at especially assault weapons,” said O’Malley, who has long favored reinstating the federal assault-rifle ban that lapsed in 2004. “You look at some of these guns, and it’s just hard to conclude that these guns should be in the hands of anyone who isn’t a soldier on a battlefield or a law enforcement officer sent into a tactical situation.”

O’Malley acknowledged that a ban on assault rifles like the one the Connecticut shooter used would be “a lot more effective on the national level.” But he said that Maryland lawmakers should consider a similar prohibition and that he would “absolutely” sign a ban if it reached his desk.

O’Malley also said state officials should consider limiting “the huge magazine clips” of the kind the Connecticut shooter used.

In addition to gun-control measures, O’Malley said his administration is exploring issues such as the appropriate level of sharing of mental-health information and standards for school safety, which he said have been mostly left to local school boards in Maryland.

In Virginia, McDonnell has asked Education Secretary Laura Fornash and Public Safety Secretary Marla Graff Decker to review recently submitted school safety audits with superintendents. He ordered the creation of a task force — made up of educators, public safety experts, legislators and others — to review school safety and make legislative and budget proposals to address any safety needs.

And he announced the creation of a position within the Department of Criminal Justice Services: the school and campus safety coordinator.