WASHINGTON — The Navy’s top leaders acknowledged on Tuesday that the country’s fleet of warships and their accompanying sailors are deeply stretched because of a combination of 100-hour workweeks, budget constraints, extended deployments and delays in training and maintenance.

But they insisted that they are not ready to say definitively that those factors contributed to four accidents in the western Pacific this year, two of which left a total of 17 sailors dead. Nonetheless, Adm. John Richardson, the chief of naval operations, promised the Senate Armed Services Committee that “we will fix this.”

In a moving tableau, visibly grieving relatives of the fallen sailors sat behind Admiral Richardson, Navy Secretary Richard Spencer and John H. Pendleton, a director at the Government Accountability Office. Their appearance lent a weight to the proceedings that seemed to cut through talk of mandatory budget restrictions imposed by Congress.

“Your presence here today reminds us of our sacred obligation to look after the young people who volunteer to serve in the military,” Senator John McCain, Republican of Arizona and chairman of the Armed Services Committee, told the family members. “It is simply unacceptable for U.S. Navy ships to run aground or collide with other ships — and to have four such incidents in the span of seven months is truly alarming.”