WASHINGTON – Sen. John Kerry has a problem with women. He’s not winning over enough of them to offset his bigger problem with men.

In Missouri, for example, the female vote split 46-41 percent for Kerry, while the male vote split 55-36 for President Bush in a mid-September survey conducted for Knight Ridder and MSNBC by Mason-Dixon. The statewide bottom line: Bush led 48-41 percent.

In Ohio, the female vote split 47-44 for Bush, and the male vote split 51-39 for Bush, the Knight Ridder-MSNBC poll showed. Statewide, the president led 49-42 percent. The survey had a margin of error of plus or minus 4 percentage points.

Surveys of 13 states expected to be close on Election Day showed that Kerry is lagging among women well behind Democrat Al Gore in 2000, who won 54 percent of the women’s vote, according to exit polls.

Bush, on the other hand, is drawing support from a majority of men in most of the 13 states, more in line with the 53 percent he managed in 2000.

Combined, Kerry’s apparent loss of support among women and Bush’s ability to hold men’s support help explain why the president had the edge as of mid-September in most of the states that will decide the election.

The main reason for the drop-off in support for Kerry: Women, particularly married women with children, saw Bush as a stronger protector against terrorism.

“Bush is doing the best he can,” said Janet Williams, 50, an operating-room secretary from Fenton, Mo. “Kerry would not be as aggressive. I don’t feel much strength coming from him. Terrorists would feel they have more of an edge with Kerry.”

That sentiment was magnified by the recent terrorist slaughter of schoolchildren in Russia, which dominated the news around the same time that American families were sending kids back to school.

“The images from Russia are very vivid to moms,” Democratic pollster Celinda Lake said.

To be sure, Bush hasn’t captured the hearts of all women.

“Kerry would do better,” said Helen Bronkhorst, 73, a retiree in Tucson, Ariz. “Bush should have finished the job in Afghanistan. He did it all wrong. I don’t approve of what Bush did in Iraq. He went in there unnecessarily.”

In one sign of the partisan reversal of gender fortune, Republican pollster Ed Goeas noted that stay-at-home moms under age 45 – a group that went for Democrat Bill Clinton in 1992 – now are breaking for Bush.

The president knows it and plays to it.

His campaign stresses security above other issues when it targets women, with its “W Stands for Women” events and marketing.

Bush’s campaign Web site, at www.georgewbush.com, stresses security first and foremost for women and families.

“For women, the stakes in the next election are high: the safety and security of our families and homeland, the future of our nation’s economy, the health and education of our children and the path we take in a global war on terrorism,” said the Web site’s page for women.

Kerry’s Web message, at www.johnkerry.com, stressed different issues.

“We need a president who will put the American government and legal system back on the side of women,” the opening of Kerry’s Web message to female voters said. “Throughout his decades-long career in public service, John Kerry has been a champion of women’s issues. He and John Edwards will commit to helping women balance work and family, expand college opportunities, protect their health and their constitutional right to choose, increase funding for cancer research, fight violent crime and close the pay gap.”

Leaders of Democratic-leaning women’s groups recently told Kerry’s campaign that terrorism was a major preoccupation for women, and that he should emphasize it more. “They said, “Talk about terror,”‘ said Mike McCurry, who was White House press secretary for Bill Clinton and recently came on board the Kerry campaign.

Kerry’s response, McCurry said, is that “the war on terror that is most significant to them is the one that the president deliberately decided to diminish” by going to war with Iraq.

To make that point, McCurry said, Kerry is trying to work on his “tonal quality.”

“There are different ways to do attack – some are fully throated,” McCurry said, and are aimed at persuadable voters. Others are softer approaches with “security moms” in mind. Over the past few days they include Kerry taping an interview with Dr. Phil, speaking to women at a Redbook-sponsored event in New York and appearing on “Late Show with David Letterman” and “Live with Regis and Kelly.”

For the Massachusetts senator to win the battleground states, said Dennis Goldford, a political scientist at Drake University in Iowa: “Kerry needs a hell of a lot stronger push from women than he’s getting.”