Encouraged by a new mood on Capitol Hill, the D.C. city Council began a new effort yesterday to eliminate the congressionally granted property tax exemptions of 31 national organizations located here. If successful, the move would force those groups to pay an estimated $2.5 million in annual District of Columbia property taxes.

Ever since the home-rule council took office in 1975, there have been efforts to remove the exemptions. But the legislation has been stalled in committee by what some supporters of the measure believe were fears of congressional reprisal.

Last month, however, two members of the House D.C. appropriations Sub-committee, Chairman Charles Wilson (D-Tex.) and Rep. Eldon Rudd (R-Ariz.), urged city leaders to either curtail or revoke the exemptions.

Yesterday, the council's finance and revenue committe held hearings on the measure, whose sponsor, David A. Clarked (D-Ward 1), said he was optimistic about the chances of passage because of the encouragement given from Capitol Hill.

That was a very different message coming from the Hill than we have perceived," Clarke said. "For Congress to be saying that . . . is a tremendously different message than we had before.

However, the message from many of the national organizations that would be affected, some of whom have social, military and special-interest outlooks, had not changed. These groups were still opposed to the measure, doubtful of its ability to increase city revenues, and certain of the harmful effects it would have on their respective operations.

"The imposition of a tax on the B'nai B'rith International Center would impose a crippling financial burden on B'nai B'rith," said Daniel Thursz, executive vice president of the center at 1640 Rhode Island Ave. NW which is currently exempt from paying $61,763 a year in property taxes.

Francis S. Greenlief, executive vice president of the National Guard Association of the United Sates, complained that, "Revocation of our tax exemption would . . . change the rules after the start of the game."

The guard headquarters, at 1 Massachusetts Ave. NW, wasgiven an exemption in 1960. If taxed at its current assessed value of $2.6 million, it would pay the city $46,665 in annual property taxes based on current rates.

"I think my organization in its 101 years has more than earned its way in support of national defense," Greenlief said.

"We can be as patriotic as the Congress can in dealing with who should be tax-exempt in the District of Columbia," committee chairman John a.

Wilson (D-Ward 2) told Greenlief.

There are 41 properties that hold such exemptions. All but 10 of those properties would probably lose their exemptions if the clarke measure passes, city finance officials said.

Among those that would lose exemptions, and the amounts they would have to pay, are National Geographic Society ($610,331), National Academy of Sciences ($483,578), National Society of the Daughters of the American Revolution ($250,710), National Education Association ($236,253) and the Veterans of Foreign Wars ($23,960).

Among the 10 that would not lose exemptions because their use would conform to other tax-exempt laws are Howard University ($2.5 million), the Young Men's and Young Women's Christian associations (about $107,000 each) and the Corcoran Gallery of Art ($148,111)9

Leo J. Ehrig Jr., Deputy director of the D. C. Department of Finance and Revenue, estimated that the city's present commercial property tax rate of $1.83 per $100 of assessed value could be lowered by 3c if the measure were enacted.

Opponents of the measure, some of whom doubted the Council's ability to enact such a law, predicted that Congress would probably reduce the city's federal payment if the measure were approved.

The payment is the federal government's annual allocation to the city to compensate the district government for the loss of revenues from tax exempt property in the nation's capital.