The governor of Bermuda, Sir Peter Ramsbotham, announced today has asked Britain to send troops to Bermuda, where police battled young blacks in downtown, Hamilton in the third day of disturbances.

Damage from rioting and fire bombs was estimated at more than $4 million.

A government statement said the request was a"precautionary measure" to prevent society forces of this British island colony from being over-extended.

About 40 policemen and troops of the Bermuda Regiment fired scores of riot gas grenades this afternoon to disperse a crowd of 300 youths massed in Court Street near the Parliament building and two blocks from the waterfront. The area is about a mile from two of Hamilton's luxury tourist hotels, the Bermudian and the Princess.

Shops on Front Street, one of Bermuda's major tourist attractions, closed early today as storekeepers hammered sheets of plywood over such major stores as Triningham's and Smith's.

One worker said: "We don't know what's going to happen, but we need the plywood up, at least for insurance purposes."

Many officials here think that the Front Street area could be a target for attacks by the arsonists who last night set more than a dozen fires.

Riots erupted Thursday night after a stay of execution was refused for murderers Erskine Burrows, 33, and Larry Tacklyn, 25. The two black prisoners were hanged at dawn Friday. Burrows was convicted of murdering Gov. Sir Richard Sharples and four other persons in 1972-1973. Tacklyn was convicted in two 1973 killings.

A spokesman for British Prime Minister James Callaghan said in London that the government was "urgently considering" the request for troops. The spokesman said he understood the request was for a company of about 100 men.

No arrests or injuries were reported in today's fighting, but some police and rioters suffered minor injuries Thursday.

The crowd today stayed about 75 yards away from police and fired slingshots filled with glass. Some youths inside and atop buildings hurled bottles and rocks. The police and soldiers wore riot helmets and carried shields, unloaded rifles and sticks.