Conservative Republican, bidding for a bigger voice in national Republican policymaking, have persuaded a Harlem backer of Ronald Reagan to challenge incumbent Mary Crisp for re-election as co-chairman of the Republican National Committee.

Their candidate, it was learned yesterday, is Gloria Toote, a black lawyer who last year seconded Reagan's nomination against President Ford.

Crisp, a Ford supporter from the Reagan stronghold of Arizona, said yesterday that her challenge has let herself be used for a "right-wing purge effort."

"It's a brilliant piece of strategy for them to put up a black against me," the Arizona national committee-woman said, "but it's really an effort to narrow the base of the party."

Toote, who held two sub-Cabinet positions in the Nixon and Ford administrations, said she was running in order to let the Republican Party "prove it has an open-door policy."

She said she believed she could "articulate the philosophy of the Republican Party to Americans of all kinds."

Crisp was named to her job by Republican National Chairman Bill Brock last year. Both Brock and Crisp are up for election at the Jan. 20 meeting of the Republican National Committee here, but no challenge to Brock has surfaced at this time.

The move to dump Crisp comes at a time when conservatives are increasingly critical of Brock's management of the national committee. Brock, in a letter to committee members yesterday, asked their support for both Crisp and himself.

Late last week, Reagan and his 1976 campaign manager, Sen. Paul Laxalt (R-Nev.), bitterly protested Brock's refusal to spend $50,000 of RNC funds to finance a Laxalt-led cross-country airborne speaking caravan of Republicans opposed to ratification of the Panama Canal treaties.

Last night, Reagan issued a statement saying he had not "withdrawn my support of the party" over the dispute.

"I shall continue to work to strengthen the Republican Party, not only by raising funds, but also campaigning for its candidates," he said. "To the extent that there is any difference, it is limited to the ways and means by which to best oppose the proposed Panama Canal treaties as they have been written."

However, Reagan aide Peter Hanaford said Reagan had not lifted his ban on any further use by the RNC of a fund-raising letter signed by Reagan on the Panama issue, which brought $700,000 into party coffers over the last two months.

Crisp has been a target of conservative criticism on a variety of grounds, including her active involvement in the women's movement and her participation in last month's National Women's Conference in Houston.

However, Toote identified herself in an interview as a "strong supporter" of the proposed Equal Rights Amendment.

Crisp said she had known for months that Franklyn Nofziger, a senior Reagan lieutenant, "was trying to find someone to run against me. Whne he couldn't get anyone on the national committee to oppose me, he went to Gloria Toote."

Toote said she had not considered running until late last week when "it was suggested that I be a candidate. They told me there were many members of the national committee who would be pleased if I ran."

The New Yorker declined to identify those who had approached her, but said of Hofziger, "He is a friend of mine and I hope he'll be one of my counselors." Nofziger was not available for comment.

Nofziger and Crisp had a public disagreement last August when the co-chairman criticized Reagan's political "purism" and charged that groups like his independent political-action committee, Citizens for the Republic, were "draining money from the coffers of the Republican Party."