President Reagan made another of his famous phone calls yesterday--this time to the man he fired as chairman of the Civil Rights Commission.

Since Arthur Flemming, who was dismissed by the president last year, recently formed a group to monitor "regressive actions" by the Reagan administration on civil rights, the call came as--well--somewhat of a surprise.

"I certainly wasn't expecting it," said Flemming, one of 400 assembled at the Dirksen Senate Office Building last night to celebrate the recent passage of the extension of the Voting Rights Act of 1965. "He said he appreciated the fact the Citizens Commission on Civil Rights was being set up, and that if we identified, at any time, failure on the See VOTING, E2, Col. 4 VOTING, From E1 part of executive branch in the area of civil rights, we should let him know."

Flemming, a gracious opponent, reserved comment on the offer and the call.

Not everyone was as polite.

"The gall of that man," fumed former Democratic congressman Father Robert Drinan. "He fires him and then offers his support."

"If he really meant the phone call, then he should put him back into a position where he could do something," said Benjamin Hooks, chairman of the Leadership Conference on Civil Rights, which sponsored the party and was a prime supporter of the Voting Rights Act extension.

An umbrella coalition of 160 public service groups, LCCR began a broad-based and intensive lobbying effort for the Voting Rights Act about 18 months ago. Despite an initially lukewarm reception by the administration, a compromise was reached and the bill signed into law June 29.

"At a time when so many are suffering from despair, the passage offers hope," said Ralph Neas, executive director of the conference.

The prime Senate supporters of the measure--Sen. Robert Dole (R-Kan.), Sen. Edward Kennedy (D-Mass.) and Sen. Charles McC. Mathias (R-Md.)--all arrived like celebrities, shook hands, slapped backs and threw lavish thank-you bouquets at each other.

There was one close call when an aide to Dole arrived a few moments before her boss and was horrified to discover that a name tag had not been made out for the senator.

"You mean a name tag was not made out for Sen. Dole?" she reprimanded. The matter was taken care of just in the nick of time, and the name tag was ready and waiting when the senator arrived.

A few minute later, everyone locked hands for a moving chorus of "We Shall Overcome," swaying back and forth "just like in the old days," as Hooks put it. There were misty eyes in the crowd.

"I wouldn't say it's an end, but it's certainly a start," said Dole. "We have to get away from the image--whether it's perceived or real--that this administration only worries about certain types of people. I think the passage of this bill and the new tax reform will be very helpful."

Hooks called the administration's stance on civil rights "not neutral, but anti-civil rights," calling some of the positions the president has taken "very, very negative."

"We've never really been satisfied with the enforcement of the Voting Rights Act," said Hooks. ". . . And as economic conditions get worse, people get mean. All I know is that we will continue to be vigilant."

"Think about this celebration," Kennedy boomed, rousing the crowd in typical convention-like fashion, "and hope the next victory we get is the passage of the Fair Housing Bill."

Everyone cheered and hugged. And then Hooks led the crowd in one final chorus. They sang loud and clear, like only true believers could:

I shall not, I shall not be moved. Like trees standing in the forest, I shall not be moved.