The board of trustees of the University of the District of Columbia passed a resolution last night saying that it wants to take over Antioch Law School and that it will "move with all deliberate speed" to carry out the acquisition.

The 10-to-2 vote came after strong support last week by the D.C. City Council for UDC to acquire the innovative 14-year-old school, which has been beset by financial and accreditation problems.

Although the action by the board of trustees stopped short of a final takeover, Antioch officials hailed it as a decisive step toward rescuing the 360-student school. Last fall Antioch University trustees threatened to close the law school, saying they were no longer able to support it.

Law school Dean Thomas J. Mack said he was confident that the City Council would approve a supplemental appropriation to cover the full cost of the acquisition, which an accounting firm placed put at $2 million.

The council voted 10 to 3 last week to add $1.3 million for the takeover to next year's city budget. The law school also will require $4 million to $9 million for new facilities, accountants said.

"We will be every excited and proud to go forward as the UDC School of Law," said Mack.

The trustees' vote came at the end of a five-hour meeting during which UDC administrators expressed concern about the long-term cost of operating the law school and doubts about Antioch's academic standing.

However, Trustee Daniel Fivel, who said he originally had been skeptical about a takeover, said he supported it because "we are saving a very important institution."

"In these Reagan years when nobody stands for anything except the almighty dollar, Antioch stands for the proposition that man does not live by bread alone. I will be very proud to be a trustee of such an institution," Fivel said.

Founded as an alternative to traditional law schools, Antioch emphasizes public-interest law, requiring students to earn about a third of their credits by handling cases for low-income clients. Its classroom building is at 2633 16th St. NW with a library in a rented mansion three blocks away.

American Bar Association evaluators have proposed removing the school's accreditation because of "deficiencies" in facilities, finances and academic standards, but the ABA has postponed final action.

Last night, Mack said he was certain that the ABA would not take such steps if the school becomes part of UDC.

However, trustee Herbert O. Reid urged board to get assurances of continued accreditation as well as full city funding before it takes the final step to acquire the law school.

In a statement to the board, acting UDC President Claude A. Ford said he feared that taking over the law school would create a "severe financial crisis" for UDC, whose current financial situation, he said, is "not sound."

But trustee Joseph Webb said he did not like such contingencies and that the board should move to take over the law school and make it "a full part" of UDC.

The two trustees who voted against the resolution were Lucy Cohen and F.D.R. Fox.