President Carter told Rep. Joseph L. Fisher (D-Va.) yesterday that he would not reopen the decision that permits Virginia to construct Interstate Rte. 66 from the Capital Beltway to the Potomac River, a spokesman in Fisher's office said.

Fisher had sought an appointment with Carter over the controversial highway at the urging of the Arlington County Board. As construction on the 4-lane highway has progressed through Northern Virginia, there has been a steady stream of protests from residents in those areas that the Virginia Department of Highways and Transportation was building the right of way wider than necessary in preparation for some day widening the road to eight lanes.

In February 1977, Transportation Secretary Brock Adams affirmed an earlier decision permitting I-66 to be constructed, but restricting it to four lanes in width. Further restrictions permit only buses, four-rider car pools and certain other vehicles to use the highway rush hour periods and ban heavy trucks outright.

Carter called Adams yesterday morning and asked him if the project was being closely monitored by the Federal Highway Administration and was being built within the terms of the agreement.

"I assured the President that it was," Adams said. He said that his department has been carefully studying the I-66 design and construction practices and that "we have no reason to suspect it isn't being done precisely by the numbers."

Carter told Fisher that I-66 had been a "close call" along with a number of other national highway projects, the Fisher spokesman said.