WASHINGTON — In a long-awaited interpretation of the new health care law, the Obama administration said Monday that employers must offer health insurance to employees and their children, but will not be subject to any penalties if family coverage is unaffordable to workers.

The requirement for employers to provide health benefits to employees is a cornerstone of the new law, but the new rules proposed by the Internal Revenue Service said that employers’ obligation was to provide affordable insurance to cover their full-time employees. The rules offer no guarantee of affordable insurance for a worker’s children or spouse. To avoid a possible tax penalty, the government said, employers with 50 or more full-time employees must offer affordable coverage to those employees. But, it said, the meaning of “affordable” depends entirely on the cost of individual coverage for the employee, what the worker would pay for “self-only coverage.”

The new rules, to be published in the Federal Register, create a strong incentive for employers to put money into insurance for their employees rather than dependents. It is unclear whether the spouse and children of an employee will be able to obtain federal subsidies to help them buy coverage — separate from the employee — through insurance exchanges being established in every state. The administration explicitly reserved judgment on that question, which could affect millions of people in families with low and moderate incomes.

Many employers provide family coverage to full-time employees, but many do not. Family coverage is much more expensive, and the employee’s share of the premium is typically much larger.