Lt. Col. Rifaat Assad, chief of Syria's security forces and brother of Syrian President Hafez Assad, two weeks ago paid $1.1 million in cash for a mansion on a quiet cul-de-sac in Potomac, Md.

State Department officials said late last week that Rifaat Assad was visiting the United States unofficially, and had come here for a private medical checkup and to enrollhis two sons in an American university.

The State Department has not initiated any contacts with Assad, these officials said, partly out of sensitivity to reports that he has been involved in brutally repressive measures against religious and political dissidents in Syria.

"He's the one who keeps his brother in place," one official said.

David T. Schneider, deputy assistant secretary of state for Near Eastern affairs, acknowledged, that he did speak with Assad at a reception given by the Syrian ambassador in Assad's honor. He would not comment on the substance of the discussion. Responding to a report that Assad had left Washington for a visit to the West Coast, Schneider said, "That may not be inconsistent with a private visit."

Assad's arrival in the United States at the height of negotiations in Lebanon set off a flurry of press reports speculating he was here to make back-channel contacts with American officials.

U.S. diplomatic and intelligence officials said it is unlikely the Syrian president would send his military-oriented brother on a sensitive diplomatic mission. But one Middle Eastern diplomat said that Rifaat Assad has been sent by his brother as an envoy to Saudi Arabia twice in the past 18 months "to arrange certain things," presumably relating to Saudi Arabia's financial aid to Syria, which is overseen by Crown Prince Abdullah, the second-ranking member of the Saudi royal family. Another report from Syria this week indicated that the Saudis have been acting as go-between in discussions with U.S. officials over the withdrawal of Syrian forces from Lebanon.

"The fact that he has been sent to Saudi Arabia recently makes it not out of the question that he has been sent for diplomatic contacts here," the Middle Eastern diplomat said.

Like Assad's itinerary, the details of last month's real estate transaction were closely held by the brokers and lawyers involved. The deal's million-dollar-plus price tag puts it among the largest residential purchases in the Washington suburbs in recent years, said Rufus Lusk III, publisher of a real estate data service. The 13,000-square-foot Georgian colonial home set on a two-acre lot has eight bedrooms, seven baths, a three-story marbled foyer and a tennis court. Built by developer William A. Miller, the house was completed three weeks before the sale.

Several diplomatic and real estate experts said that while there has been a great increase of Middle Eastern investments in U.S. real estate in the past 10 years, investors from Syria, which does not enjoy the immense oil wealth of many other states in the region, have generally stayed away.

The Potomac real estate broker who handled the sale, Farid Srour, said that Assad had supervised the formation of a Maryland-chartered corporation, DMS Freres Inc., to make additional real estate investments in the United States. "It's going to be very active in business," he said.

Rifaat Assad's name did not appear on the contract for sale or the deed that was issued under Montgomery County commercial listings in the name of DMS Freres, which is not required to list its officers and directors until April of next year. Assad made the $1.1 million offer -- $100,000 less than the asking price -- on Aug. 19 and the deal was consummated the next day at a settlement attorney's office in Rockville with a $1 million cashier's check drawn on the Potomac Valley Bank.

Dennis Homberg, the bank's president, said he believed the funds were transferred by wire from overseas. "I really don't have much experience with this sort of thing. We simply don't see those kinds of funds go through the bank like that."

A broker for the Potomac branch office of Shannon & Luchs, which split the $60,000 commission on the sale with Srour, said he was kept in the dark about the identity of the purchaser from the beginning, but was later told by Srour that the buyer was a "high political official from Syria."

The attorney who handled the settlement, James H. Murdock, said, "I was instructed not to talk about it. I'm not trying to be a stinker, I just can't help you."

Srour said he was told that Assad's two sons were expected to enroll at George Washington University this fall. He also said that Assad himself had left the Washington area last week for a trip to the West Coast. Before he left, Assad was given a medical checkup by an unidentified Potomac physician.

"I translated for the doctor during the checkup. He's my neighbor," said Srour, who is of Syrian ancestry. Assad "is just fine. He looks handsome and is a very nice man."

When two reporters visited the residence earlier this week, there were about a half dozen people visible in the house, including a young man who was identified as Assad's son. An unidentified aide said that Assad was not there and that he was "under a doctor's care," while in this country.

"Sometimes he doesn't even tell me where he is going," the man said. Parked in front of the house was a new Porsche 911 sports car, two new Mercedes Benz automobiles and two new American luxury sedans.

The wide open landscape surrounding the Potomac residence is in sharp contrast to the Assad family's barricaded villa in Damascus, located adjacent to the U.N. headquarters for the Golan Heights peace-keeping force. Eyewitnesses reported earlier this year that following an upsurge of opposition to the Assad government, makeshift ramparts studded with antitank traps have been constructed along the three-lane highway in front of the villa. In addition, machine-gun nests were positioned atop surrounding buildings and a company of tanks was stationed behind the villa to deter any assault.

In eyewitness accounts and diplomatic reports reaching U.S. and European capitals during the spring of 1981, Assad was reported to have commanded teams of Syrian special forces troops who massacred scores of men in the city of Hama. The assault reportedly was part of a crackdown on religious and political opposition to his brother's minority Alawite Moslem rule in a nation populated by a Sunni Moslem majority.

While some U.S. officials were surprised that Assad may be planning large investments in the United States, others noted that Assad's financial dealings in Syria and Europe have been the subject of diplomatic curiosity in the past.

"No matter what they say about us, if they can get their kids into schools here or their money out, they all try to come to the United States," said one senior official.

Added Nachman Shai, press counselor at the Israeli Embassy, "It's always good to invest in real estate in this country for a rainy day."