Two members of a fledgling unofficial peace committee were arrested today in an apparent move by security police to stamp out the dissident organization involving about a dozen Moscow intellectuals.

The committee was organized 10 days ago by 11 persons who marked the current U.N. session on disarmament by issuing an appeal to the governments and peoples of the Soviet Union and the United States.

The appeal, issued to Western correspondents here, called for the banning of nuclear weapons and for a "free exchange of opinions" between the two countries. It also urged that the public in both countries be informed about "disarmament issues."

Members of the committee were warned by the authorities last week to end their activities in affairs that "do not concern" them, according to a spokesman for the group.

Several members had been taken into custody over the weekend, but were released with a warning that their continued activities could lead to criminal charges. One of the members was in telephone contact with an unnamed group in Boston and his telephone was cut off.

Plainclothes and uniformed police today arrested Sergei Batovrin, 25, an artist in whose apartment the committee had met, and Sergei Rosenoer, 29, a mathematician.

Apart from the 11 founding members, the committee has been able to get only 16 other Soviet citizens to sign their appeal.