U.S. officials accompanying Secretary of State Alexander M. Haig Jr. expressed concern today that renewed fighting in Lebanon could rekindle the uncontrollable killing of that country's 1975-76 civil war and threaten to grow into a wider Middle East conflict.

The week-old fighting, which prompted a flurry of U.S. diplomatic efforts and a public expression of apprehension from Haig, places Lebanon "right on the brink of a major outbreak of hostilities," according to a senior American official.

Haig, at a press conference this morning in Jerusalem, put the blame for the outbreak on Syria. Speaking of the shelling of the predominantly Christian Lebanese city of Zahle, Haig said, "We view the brutality of the Syrian action against the Christian enclave as a very, very serious turn of events which is unacceptable by any measure of appropriate international standards of conflict."

A State Department official who participated in Haig's meeting with Prime Minister Menachem Begin and other Israeli officials spoke to reporters afterward of "great pressure building in Israel to do something to protect the Christians" in the absence of a binding cease-fire. Direct Israeli involvement against the Syrian armed forces could court a military response from Damascus.

After flying to Jordan, Haig discussed the Lebanese fighting, along with other issues, in a meeting with King Hussein. Jordanian officials said the Lebanese outbreak is being taken very seriously here but they spoke strongly against Israeli intervention.

Haig and Hussein talked more than two hours today and the meeting was said on both sides to have been a frank airing of views. There was no indication of any change in Hussein's refusal to join the Camp David process or in his rejection of bringing Jordan into negotiations with Israel without participation of the Palestine Liberation Organization.