CORAL GABLES, Fla. -- With worries about terrorism heightened following attacks in France and California, baseball owners began their two-day meeting Wednesday by discussing threat protection with the U.S. Homeland Security secretary.

Presenting more than 2,400 games a year in venues that attract large crowds, Major League Baseball has tightened checks in recent years. Starting last year, fans were required to go through metal detectors at all 30 ballparks.

"There's got to be more security than there is now. I don't know what it will be," Chicago White Sox owner Jerry Reinsdorf said Wednesday. "Everybody realizes that the world has changed and these people are never going to give up, so we have to give up some of our comforts."

After arriving in a seven-car motorcade, Homeland Security Secretary Jeh Johnson addressed owners for approximately an hour and took about a half-dozen of their questions. Teams want to know what layers to add.

"His message was more of the same: Recognize the new realities," Atlanta Braves chairman emeritus Bill Bartholomay said. "Radicalization is something that doesn't necessarily have to take place outside the United States."

Bartholomay said Johnson cited the December attack in San Bernardino, California, as an example. Johnson did not stop to speak with media when he left the building.

"He pointed out some very interesting things that we all need to pay attention to, because we are part of maintaining public safety," Miami Marlins president David Samson said. "What we try to do is walk the line between safety and enjoyment. ... The balance is really hard to walk, and what Secretary Johnson pointed out is that our most important job is to walk that balance and to be very aware when you're getting too far one way or the other."

According to Samson, Johnson told the group a stadium could be 100 percent secure if additional steps were taken, such as prohibiting fans from bringing any bags and eliminating food and food-services workers. Checking the trunks and bottoms of cars entering parking lots outside ballparks could be another step discussed at some point.

Cubs president of business operations Crane Kenney said last weekend that the team is working with the city of Chicago to try to limit game-day traffic on Clark and Addison streets outside Wrigley Field to emergency vehicles, city buses and pedestrians.

At many ballparks, there is no room for a larger security perimeter.

"Our space outside the stadium is pretty cramped, but we're going to do what we're asked to do," Yankees owner Hal Steinbrenner said.

The meetings, which end Thursday, are the last before the likely start of collective bargaining with the players' association for a labor contract to replace the deal that expires next Dec. 1. Even before talks with the union, owners have to determine their bargaining positions on key economic issues such as revenue-sharing, the luxury tax threshold and rates, and whether management wants to push harder for an international amateur draft.

Management and the union have spent the offseason discussing whether a rules change is needed for 2016 to protect middle infielders at second base from oncoming runners.