LAKE SUCCESS, N. Y., November 5--The Steering Committee of the United Nations Assembly tonight approved a United States proposal to widen the permanent headquarters site question to include consideration of New York City end San Francisco.

After debating at length a Soviet Ukrainian Proposal to include Europe as a possibility for the temporary or permanent headquarters of the United Nations., the 14-man committee voted it down 7 to 2, with Russia and the Ukraine alone favoring it. Three committeemen abstained.

Then the committee by an eight to three vote the proposal of former Senator Warren it. Austin, Chief V. S. delegate, opening the headquarters question to include invitations from New York City and San Francisco. There was one abstention.