U.S. Ambassador Nicholas A. Veliotes' blunt and indignant demand that the Egyptian government "prosecute those sons of bitches" who killed an American tourist came as no surprise yesterday to those who knew this veteran diplomat in previous governmental posts.

"He's a very emotional and human guy who never watched his language all that carefully," said Morris Draper, a State Department officer who was a Middle East troubleshooter while Veliotes served in State's top Middle Eastern policy job, that of assistant secretary of state for Near Eastern and South Asian affairs, from 1981 to 1983.

"I can't think of a better guy to play the tough cop with a heart of gold -- he'll scream and yell at them, but the Egyptians know he is their friend," said Geoffrey Kemp of the Georgetown Center for Strategic and International Studies, who was the National Security Council staff officer on the Middle East when Veliotes was State's Mideast chief.

"He was awfully good at getting very angry at foreign leaders in a genuine and effective way, but this was less effective within the bureaucracy," Kemp noted.

Veliotes' predecessor in State's top Mideast post, Harold Saunders of the American Enterprise Institute, called Veliotes' reaction aboard the Italian liner Achille Lauro "very characteristic" of the man. "Undoubtedly, in a situation like that, he said what a lot of us would feel like we ought to say," said Saunders.

Veliotes, 56, is a fiesty Californian of Greek descent who has been a career Foreign Service officer for 30 years and has served in a var- iety of important diplomatic posi- tions, including deputy chief of mis- sion in Israel and ambassador to Jordan.

While outspoken and sometimes garrulous in private, Veliotes has usually been extremely cautious in his public utterances. It was not clear that Veliotes realized Wednesday that his tough remarks over a ship-to-shore radio from the Italian liner would be overheard by journalists and transmitted almost instantly throughout the world.

In an incident in 1984, candid comments of Veliotes to members of Congress became public in a way that stirred controversy on Capitol Hill. The issue was a bill to move the U.S. Embassy in Israel from Tel Aviv to Jerusalem, which was opposed by the State Department on grounds it could provoke a wave of anti-American violence throughout the Islamic world.

In what he thought was a private meeting, Veliotes reportedly asked senators for advance notice before a Jerusalem move, so he could evacuate from the Cairo embassy. Some lawmakers were angered by what they considered to be Veliotes' scare tactic; others were sobered by it.

Veliotes was brought into the top Mideast job by Secretary of State Alexander M. Haig Jr. at the beginning of the Reagan administration after Haig decided it was essential to have a career professional in the post. The two were never close, however, and by early 1982 Haig made it clear he planned to replace Veliotes.

Haig, though, was ousted first, in June 1982. Veliotes served as assistant secretary for more than a year after George P. Shultz became secretary of state, and was sworn in as ambassador to Egypt on Oct. 28, 1983.