FLORENCE, S.C. (AP) _ Several members of an American Legion post resigned after the organization refused to admit a black member.

At least two of the post officers and one member quit after six members of the Fred H. Sexton Post 1 voted against the black applicant at a July 3 meeting, the Florence Morning News reported today. Only two votes are required to reject an applicant, the News said.

''I don't want one in here,'' past Post Commander William D. Leftridge said during a debate over the application of a black Vietnam veteran, according to the minutes of the meeting. ''For 70 years since the post was chartered, there hasn't been one in here and I don't want to see it now.''

Leftridge did not return telephone calls today.

The Morning News said at least three members of the post resigned, and WDAR radio in Darlington quoted unidentified sources as saying that six members had resigned.

The black applicant, Thurmond L. Thompson, is a Vietnam veteran who works at General Electric Co., the radio station reported.

Besides Leftridge, other post members said at the meeting they could not vote for a black.

Florence has two American Legion posts. Post 1 has no black members and Post 228 has no white members.

The American Legion's national headquarters in Indianapolis asked the South Carolina headquarters to begin an investigation into the incident, said Phillip Onderdonk, the organization's judge advocate. The post could lose its charter, he said.

A telephone call to B.L. Black, the department adjutant of the state American Legion, was not immediately returned.

Some American Legion members said the opposition to Thompson stunned them.

''I was sitting there like a lot of the other members - in shock,'' said Ken LaFevor, a post member who resigned soon after the meeting.

''There's one color in the military and that was green. And I know we all shed the same color blood,'' said LaFevor, who was a member of the post for about 18 months.

''I was really hurt. I just couldn't believe what I was hearing,'' said local post 2nd Vice Commander James N. Maurer, adding he resigned immediately after the meeting.

Maria Lewis, the former post secretary who remained a member, said Wednesday that it is against state bylaws to integrate the Legion. She is the Florence County veterans affairs officer.

''We have to keep a black post and white post separate, and when we have conventions we will all combine. But as far as blacks coming in here to be our members, they don't want us to join their post and we can't have them join ours,'' Lewis said.

The Legion has allowed blacks since it was first created in 1919, Onderdonk said.