Two Allstate Insurance Co. executives agreed yesterday to consider relaxing the company's rule that new applicants for renters' insurance in the District of Columbia must have someone in their homes 24 hours a day.

The requirement was imposed last November, company officials said, because of high theft losses and low ceiling rates in the District.

James Montgomery, the D.C. insurance superintendent, met for two hours yesterday with the two Allstate executives, Frank R. Montgomery (no relation) and Gene E. Mulligan, who came from the company's headquarters in North Brook, Ill., to discuss the requirement. Superintendent Montgomery had requested the meeting after expressing concern that the rule might discriminate unfairly against renters who work or attend school and are gone from their homes during the day.

Existing Allstate policyholders in the District are not affected by the 24-hour requirement. It applies only to those seeking an Allstate renters' policy for the first time in the District of Columbia.

In adopting the rule, Allstate departed from the way it typically operates elsewhere and from the procedures of other major insurers such as State Farm, Geico and Aetna. The procedure normally is to offer insurance at regular rates to renters who have someone at home during the day and, in cases where they are not home, to issue the policy at a higher rate.

During the meeting, Superintendent Montgomery asked Allstate to consider introducing a policy with a larger theft-loss deduction--the threshold amount above which the company is responsible--and a lower premium. A second possibility, he said, would be for the company to accept other security measures, such as deadbolt locks or building security systems, in cases where the tenant's home was vacant during the daytime.

"They said they would give serious consideration to these options," Montgomery said. He said Allstate agreed to respond within 30 days.