A Ku Klux Klan group received one permit yesterday to hold a rally near Rockville Saturday and applied for a second, for a rally in downtown Washington on Nov. 27.

The permit for a "Support Your Police" rally this weekend was issued to the Invisible Empire of the Ku Klux Klan by Montgomery County Parks director Stan Earnst.

On Wednesday, Earnst approved a joint permit for two local groups that oppose the Klan to hold a counterrally Saturday morning.

Saturday's Klan rally will be in Lake Needwood Park, north of Rockville, in the afternoon, while the counterrally will be held six miles away, in Woodside Park in Silver Spring.

The Knights of the Ku Klux Klan had initially planned to hold a rally in the District on Nov. 6, but canceled those plans late last month.

Klan officials said lack of organization was one reason for the cancellation. Another was competition from a variety of anti-Klan activities hastily scheduled at virtually every rally site in Washington shortly after Klan officials announced their intention to apply for a rally permit.

The Washington anti-Klan activities, including a downtown march and rally and a program of food distribution, education and prayer, are scheduled to go ahead Saturday as planned.

Klan Imperial Wizard Don Black said in a WJLA-TV interview yesterday that the Klan intends to hold a rally in Washington on Nov. 27.

The National Park Service said the group applied today for a permit for a rally in Lafayette Square on that date, and that the request is under review.

Black participated in the television program with Georgia State Sen. Julian Bond, past president of Klanwatch, and the Rev. Ernest R. Gibson, director of the Council of Churches of Greater Washington, which is participating in Saturday's anti-Klan activities.

About 50 demonstrators marched outside the station to protest the Klan's activities.

"We want people to know the citizens of Montgomery County hold far different views than the Ku Klux Klan," said Stan Gildenhorn, a Silver Spring attorney and former chairman of the county Democratic Party, who organized the Montgomery County Committee United Against Hatred last week.

His group, a collection of labor, church and civic groups, has joined forces with the All People's Congress, a lobbying group, to protest the Klan's presence in the county.

Barbara Davidson of Takoma Park, local coordinator of the congress, said the group was formed to protest many of the Reagan administration's policies.

"There will be very tight security," said Pat Plunkett, a spokeswoman for the Maryland National Capital Park and Planning Commission.

He said both park and county police will screen vehicles entering the Klan rally.

Samuel Royer of Rohrersville, in Washington County, who initially filed a rally permit on behalf of the Klan, told the commission that about 35 robed Klansmen will be present at the rally and that Klan literature will be distributed to those attending.

"According to other rallies we have held throughout Maryland, we anticipate a crowd of approximately 150 people."

Royer could not be reached to list those prior rallies.

The Klan permit initially was denied because it was not filed in time to meet the 30-day limit required of noncounty residents, said Norman L. Christeller, chairman of the park commission.

The Klan permit was resubmitted Monday by Michael Griffith of Gaithersburg, who said Bill Wilkinson of Louisiana, the Imperial Wizard of the Invisible Empire, will speak. Neither could be reached for comment.

"I'm confident everything is going to be under reasonable control," said Christeller. "I trust we won't have people imitating the Klan's past activities and engage in violence."

The anti-Klan rally in Montgomery County will be held from 10 a.m. to noon. The Klan rally is set for noon to 2 p.m.