The United States has quietly joined the list of countries expressing concern to Pakistan over the death sentence handed down to former prime minister Zulfiqar Ali Bhutto.

The State Department confirmed yesterday that the United States had taken the step through its embassy in Rawalpindi, but no details were released. One State Department official said the appeal had been made on "humanitarian" grounds.

U.S. - Pakistani relations hit a low point just before Bhutto was over-thrown last year but the two countries have maintained generally close ties over the years because of Pakistan's links to China and Washington's desire for a general balance of power on the Indian subcontinent.

A number of countries throughout the Middle East and neigboring Iran have appealed to the government of Gen. Zia ul-Haq to spare Bhutto's life.Generally, principles of "Islamic compression" have been cited, but there is known to be concern, particularly in Iran, that extreme political violence could erupt in Pakistan if the sentence is carried out.

Iran, which is facing considerable unrest of its own, is nervous about possibly destabilizing impact the execution might have throughout the region.

State Department sources said that Saudi Arabia, Libya, Iraq, Egypt, Kuwait, Romania and Turkey have also made public or private appeals to the Pakistanis.

U.N. Secretary General Kurt Waldheim and Amnesty International also have made appeals.

One U.S. official said that the Pakistanis are adamant on the judicial process being allowed to go through its normal course, but indicated that ultimately a serious political questional faces the Pakistani government.

"What do you do with a former premier you've overthrown?" the official said. "It's like riding a tiger. How do you get off? He could come back to power."