Hill & Knowlton has received $5.64 million for helping Kuwait spruce up its image in the United States since the Iraqi invasion, according to the public relation firm's report on its lobbying activities filed with the Justice Department.

The sum includes $2.7 million for expenses such as placing newspaper advertising and organizing pro-Kuwait speeches, art exhibits and other events designed to gain American sympathies for occupied Kuwait.

Another $2.9 million went to salaries for Hill & Knowlton employees and individuals who worked on the account at other organizations. A Hill & Knowlton spokesman said 75 employees of the firm have worked on the project, including Robert K. Gray, founder of Gray & Co., which merged with Hill & Knowlton in 1986, and who served as President Ronald Reagan's 1981 inaugural committee co-chairman, and Craig L. Fuller, chief of staff to then-Vice President Bush.

The bill was paid by Citizens for a Free Kuwait, a Washington-based group of Kuwaiti refugees in the United States. Most of the money came from wealthy Kuwaitis in Europe, according to a Free Kuwait staff aide.

The sum is one of the highest an American public relations firm has received for a single job over such a short period.

Hill & Knowlton received an average of $75,200 for every employee who worked on the account over the past 3 1/2 months, including secretaries. And the bill is mounting. "We're continuing to work and to earn money for it," said Frank Mankiewicz, a senior Hill & Knowlton executive.

"I suppose it's a lot of money," Mankiewicz said. "But that depends on what you think of what it's being spent on. We think it's a worthy cause."

"It's a ridiculous sum of money no matter what you think of the cause," said Rep. James A. Hayes (D-La.), who said his constitutents are concerned about the issue of foreign lobbying. "I resent that on an issue that should be decided by information from experts so much is being spent to influence me and the American public. This serious cause is being advertised like T-shirts or basketball shoes. That's immoral."

Public support for Kuwait's cause has been strong since the Aug. 2 invasion. But critics of the military buildup in the Persian Gulf have pointed out that the Kuwaiti government is not democratic and that support for Kuwait is coming largely from Washington.

Much of Hill & Knowlton's efforts have been geared toward combating such views. For example, it paid $1.1 million to the Wirthlin Group, a polling company, for studies showing that there is international support for Kuwait.