During a panel, Mr. Kelly said that President Trump was “contemplating issuing a tighter, more streamlined version” of the order, which has been suspended by federal courts.

Enforcement of the earlier order was marked by confusion and distress, leaving many of the affected travelers stranded overseas. “I will have, this time, the opportunity to work on a rollout plan,” Mr. Kelly said.

The new approach, he said, would try to ensure that no travelers were caught in transit, as they had been under the first executive order. “If they are in motion from some distant land, when they arrive they will be allowed in,” Mr. Kelly said. He said that would apply to both green card and visa holders.