Emanuel S. Savas, a chief architect of the Reagan administration's policy of reducing federal aid to the cities, has charged the government for 20 trips to New York in 10 months, spending each weekend at his home in Tenafly, N.J., after conducting what he described as official business.

Savas, assistant secretary of housing and urban development for policy development and research, was reimbursed for the frequent round-trip flights from Washington and for some taxi rides to his New Jersey home. He did not charge the government for the time he spent at home.

All together, Savas charged the government more than $14,000 for official trips last year, including two visits to Paris, two to London and one to Athens, according to expense vouchers filed with the Department of Housing and Urban Development.

Savas helped write a draft report on urban policy for President Reagan that upset many of the nation's mayors last summer by calling them "wily stalkers of federal funds." The White House said the document did not represent administration policy.

Because of the controversy, Savas cut short a HUD-financed stay in Paris to return to Washington. Savas said he was on a three-day vacation with his wife during a break from official business.

Asked yesterday about his trips to Europe and elsewhere, Savas said one of his main responsibilities is "the proper articulation and presentation of the policies of the administration."

Savas said that he visits his family in New Jersey every weekend and that it is cheaper to combine these visits with New York-area speaking engagements. "Here's a way of doing my job and saving the taxpayers money," he said. "If I want to do a speech, I try to schedule it for the weekend. I've been turning down midweek invitations because I've been concerned for efficiency. I do it in a way that minimizes HUD costs because there's never any food costs or hotel costs."

Other senior HUD officials also maintained an active travel schedule last year, according to the department's expense vouchers. HUD officials said yesterday, however, that the department's total travel budget dropped from $16.1 million to $13.8 million last year.

Undersecretary Donald I. Hovde, who is from Madison, Wis., made nine trips to Madison last year on official business, seven of them including weekends. Hovde, who also visited Milan, Italy, last year, said yesterday these were all legitimate trips to speak to realtors, builders and civic groups.

In August, HUD Secretary Samuel R. Pierce Jr. took a 30-day official trip to China, Japan, Hong Kong, Singapore and Egypt, where he met with housing and diplomatic officials, toured redevelopment projects and discussed possible trade and mortgage arrangements with the United States.

Since the Reagan administration took office, HUD has raised rents for indigent public housing tenants from 25 to 30 percent of their income, cut back on urban development grants and all but eliminated new construction of subsidized housing. Savas has argued that cities have become too dependent on federal grants.

Savas, who worked for former New York mayor John Lindsay and later became director of Columbia University's Center for Government Studies, said in a recent book, "Privatizing the Public Sector--How to Shrink Government," that government should relinquish its role in such areas as garbage collection and public housing to private concerns to handle these tasks more efficiently.

From March through December, nearly all of Savas' trips to the New York area began on a Thursday or Friday. Many of his expense vouchers list groups and officials he was visiting and activities such as testimony before the New York Legislature, a speech on urban enterprise zones in Brooklyn, a meeting with officials at the City Club, a tour with the mayor of Jersey City and lectures at the City University of New York, Princeton University and the American Jewish Congress.

On several vouchers, Savas said only that he was "to meet with officials in New York regarding urban policy and related matters." He said yesterday that these were mainly New York City housing officials and mayoral aides.

Several New York-area officials said Savas had come at their invitation. "He's from the area, so when we suggested a meeting, he was very willing to do it," said a spokesman for Jersey City Mayor Gerald McCann. "He agreed to it right away."

According to the vouchers, Savas spent one weekend at his Tenafly home in March, three weekends in April, three weekends in May, one each in June and July, two in August, two in September, three in October, three in November and one in December. These visits included Memorial Day weekend and Thanksgiving. Savas generally listed "lodging at no cost to the government."

Savas' expenses for each trip usually ranged from $78 to $235, covering fares on the Eastern Airlines shuttle, a cheaper New York Air flight or another regularly scheduled airline. On one October trip, he said it was "advantageous to the government" for him to stay in New York until Monday to catch a $29 flight.

The vouchers show that Savas generally had a government car drive him between HUD and Washington National Airport. He occasionally charged HUD for taxis to his New Jersey home. One voucher called taxis the "cheapest means of transportation."

During 1982, Savas also visited Las Vegas, Dallas, Cleveland, Boston, Hyannis Port, Los Angeles, Santa Barbara and Williamsburg, Va. He took a $40 taxi ride from Airlie House in Warrenton, Va., saying a HUD driver was not available and that "traveler was not familiar enough with the area to chauffeur himself to Warrenton, Va."

Savas went to Paris in June and November as an American delegate to seminars on urban problems at the 24-nation Organization for Economic Cooperation and Development. He visited Athens in March for a "seminar on public-private cooperation" arranged by the same group.

Savas said his two trips to London were to examine urban enterprise zone sites in Britain, meet with housing officials and speak at the Adam Smith Institute and at another conference. He said part of the trips were paid for by British national and local governments.

"As a principal architect of the enterprise zone proposal, I had to see the British enterprise zones firsthand," Savas said. "It was very, very useful."

Undersecretary Hovde took 11 trips to Wisconsin last year, including nine to his home town of Madison to address such groups as the Wisconsin Realtors Association, Greater Madison Chamber of Commerce, Wisconsin Real Estate Conference, Downtown Executives of Wisconsin and Hillandale Shopping Center.

Hovde said yesterday that his son is enrolled at the University of Wisconsin at Madison, but that "any personal trip I've paid for out of my own pocket."

Hovde said he turns down two of every three invitations, but that "when you come from a given community, everyone wants to identify with you. You walk the fine line of ignoring them or overcatering to them. If I were to accept every invitation from Wisconsin I'd be spending my career there, and I just can't do that."