WASHINGTON — A strike by telephone unions against Verizon Communications crept into its second work week Monday, with the two sides at odds over a revised contract proposal now on the table.

The distance between the parties dashed hopes that 87,000 Verizon workers on strike since Aug. 6 would soon leave the picket lines and return to work.

Company officials said the new offer, delivered to unions over the weekend, sets the right balance between providing strong customer service and managing the demands on workers.

"We believe we have fairly addressed the issues,'' Verizon spokesman Eric Rabe said Monday.

In contrast, the unions continued to argue that the proposal fails to address key stumbling blocks.

"The company has not proposed anything that would move negotiations along in the areas of overtime and job stress,'' said Candice Johnson, spokeswoman for the Communications Workers of America, one of the two bargaining unions.

Currently, the company can require employees to work 10 extra hours a week during seven months of the year, and 15 extra hours a week during five months of the year.

The union says that provision was intended to give the company flexibility during emergencies or periods of heavy traffic, not to allow Verizon to demand that employees work to these limits each week.

"Two hours every day is just a little bit too much for a working mother,'' said Verizon worker Lisa Charles of Newark, N.J., who has two children. "You're exhausted.''

Charles, who processes orders from other local phone companies seeking to lease Verizon's lines, said she typically works 10 hours of mandatory overtime weekly and is sometimes asked to come in on weekends.

The company says overtime is part of its multipronged strategy to meet customer demand in a tight labor market while minimizing employee stress. Other components of this approach include limiting the monthly transfers of customer service representatives, particularly in call centers with heavy volumes, and being able to distribute work such as incoming calls to centers throughout the company's region, Verizon officials say.

Verizon, the nation's largest local telephone company, is the product of a summer merger between Bell Atlantic and GTE.

But these interconnected management techniques have prompted other concerns by the unions. CWA leaders say a company proposal that would limit to 1.5 percent the number of workers that can transfer each month would trap workers in high-pressure jobs. The unions also fear that the company will reassign work to areas in their merged territory where labor is cheaper.

The International Brotherhood of Electrical Workers is striking along with CWA.

The strike affects Delaware, Maine, Maryland, Massachusetts, New Hampshire, New Jersey, New York, Pennsylvania, Rhode Island, Vermont, Virginia, West Virginia and Washington, D.C.