The Fairfax County Board of Supervisors, responding to reports of half a dozen recent hate incidents, yesterday endorsed a move to stiffen state laws prohibiting racial and religious intimidation.

The legislation, sponsored by State Del. Kenneth R. Plum (D-Reston), would establish desecration of places of worship as a specific offense and make it a felony to place a swastika on a place of worship or on any religious grounds.

Supervisor Martha V. Pennino (D-Centreville) called the recent incidents "extremely troubling" and directed the county staff to determine whether the county can enact local legislation more far-reaching than the bill Plum is sponsoring in the General Assembly.

The incidents listed by the supervisors yesterday apparently reflect a trend noted elsewhere in the Washington area recently:

* Since last June a foreign family living in McLean has been subjected to cross burnings, property destruction and general harassment.

On Dec. 9 their lawn was set afire. Both police and fire departments are investigating.

* A black family in the Burke area had "KKK" painted on their asphalt driveway.

* In three separate incidents, swastikas were painted on an outside wall of the Northern Virginia Hebrew Congregation, a traffic control box at Sunrise Valley Drive and Reston Avenue and J. E. B. Stuart High School in Falls Church.

* The county's Human Right's Commission investigated allegations of verbal harassment, use of anti-Semitic language and property destruction in a conflict between a Jewish family and a non-Jewish family in the McLean area and negotiated an agreement between the families.

The supervisors were told yesterday that police and other agencies have been directed to record and investigate hate incidents, make reports to the Human Rights Commission and hold periodic meetings on the problem.

In Maryland, reported anti-Semitic incidents increased from fewer than 10 in 1980 to 51 in 1981, according to the local office of the Anti-Defamation League of B'nai B'rith.

No anti-Semitic incidents were reported in the District of Columbia in 1981, while in 1982 there were at least seven.

In recent months, swastikas and "KKK" have appeared on synagogues, schools, Jewish delicatessen in the Maryland suburbs, and a burning cross was discovered in Rockville last fall.