The State Department, in a pointed reference yesterday to presidential candidate Edmund G. Brown Jr. and former secretary of state Henry A. Kissenger, called on "politicians and former statesmen" to hold off on public statements that could endanger the lives of American hostages in Iran.

Tension over the hostage situation remained high both in the United States and in Iran yesterday. Administration officials said they could not predict when the 61 hostages held captive at the U.S. embassy in Tehran would be released, and the first fatality was recorded in connection with anti-Iranian protests that have swept the United States since the hostages were taken a week ago.

"I think it would be extraordinarily useful if politicians and former statesmen could somehow refrain from attempting to capitalize in any way on this situation for their own advantage long enough for these people to get out alive," State Department spokesman Hodding Carter told a briefing yesterday.

Brown, appearing on"Meet the Press" (NBC, WRC) earlier called on Americans to "walk and pray throughout this country" Monday. Such a demonstration, Brown said, "would show we would be prepared to sacrifice even the cutoff of our oil to protect our own nation as a strong independent force and not one to be pushed around or be blackmailed."

At a news conference in Texas Saturday, Kisinger said the United States had a "duty" to grant poltical asylum to the deposed shah of Iran. Kissinger also said he favors deporting Iranians who break U.S. laws.

President Carter has ordered the Justice Department to begin deportation proceedings against Iraian students who violated the terms of their entry visas into the United States. But a Justice Department official said yesterday that the earliest that such deportation could take place would be December.

"We are certainly not going to see any actual deportations within a month," said the official. Carter's order was given Saturday in an effort to hold down demonstrations against U.S. policy by Iranians here as well as potentially violent counterdemonstrations.

Meanwhile, violence connected with the hostage situation escalated around the United States yesterday.

Denver police said an Iranian college student will be arraigned today in connection with the fatal shooting of a 15-year-old youth and the wounding of two companions. The three youths and other allegedly showed up outside the Iranian's apartment early yesterday to harras him, police said.

The White House, which has been concerned about the growing anti-Iranian backlash, announced that FBI agents have been detailed to investigate the Denver shooting.

According to police, the youths picked out the apartment of Afshin Sharaiati in southwest Denver from his name on the mailbox and then smashed a picture window in the third-floor apartment.

Shariate, a 20-year-old chemcial engineering student married to an American, allegedly ran from the apartment and fired at the fleeing youths with a rifle, police said.

The incident capped two days of anti-Iranian demonstration around Cororado.

Police in Huntsville, Ala., arrested two Ku Klux Klan members yesterday during an anti-Iranian rally there.