Attorney General Edwin Meese III approved a $580,000 grant yesterday for a coalition that aids battered women, ending a two-month delay in which conservatives denounced the group as radical feminists opposed to the Reagan administration.

The National Coalition Against Domestic Violence, an advocacy group representing most of the nation's 877 women's shelters, was scheduled to receive the Justice Department grant in June. But Meese took the unusual step of delaying the award after conservative lawmakers and activists complained about the coalition.

Meese's decision was a victory for Assistant Attorney General Lois Haight Herrington, who encouraged the coalition to apply for the two-year grant and lobbied hard within the department to salvage the effort. Herrington, a victims'-rights advocate ordinarily popular with the right, came under fire from conservatives for backing the coalition.

Herrington said yesterday that "the conditions are very tightly drawn on the grant" and that the coalition must comply with the restrictions to receive the second year of funding.

The grant was less than the $625,000 initially awarded, she said, because the training programs have been shifted to the Federal Law Enforcement Training Center in Glynco, Ga., and the government, not the coalition, will distribute the materials produced.

Asked why the grant was so controversial, Herrington said: "I think people had misconceptions and misunderstandings about shelters . . . . Some people really did feel shelters were anti-family. This is pro-family. You can't get families back together until you stop the violence."

Herrington also said ideological criticism of the group was misguided. "The soldier in the field is not going to question the political views of the person who comes to his aid," she said. "I don't see that this is a terribly liberal organization, and I certainly don't see that the percentage of lesbians is any greater than the national norm."

A spokeswoman for the group, which has a $102,000 annual budget, said it is pleased with the outcome.

The grant is to finance education and training programs aimed at helping abused women, a referral service for victims, and cooperative efforts among shelters, police, hospitals, businesses, schools and churches.

Patrick B. McGuigan of the conservative Free Congress Foundation, one of the first to complain to Meese about the grant, called the decision "a great disappointment. We are in the fifth year of the Reagan revolution, and not only is funding of the left continuing, this is brand new money."

McGuigan said Meese went along with the grant because "Lois is an old friend of his. She has ill-served him."

The coalition has a lesbian task force that deals with such issues as discrimination against lesbian shelter workers and fear of homosexuals.