PHOENIX — The state Court of Appeals refused Friday to lift its 2-day-old ban on a state law that allows politicians to take more money from contributors.

After a hearing by telephone, the judges rejected a claim by the attorney for Republican legislative leaders that their Wednesday order unconstitutionally infringes on the First Amendment rights of candidates.

Mike Liburdi had argued that limiting donations to the amounts that were in place until a month ago makes it impossible for candidates to wage effective campaigns.

But the judges did clarify their original order to spell out that Wednesday’s ruling only affects donations to those seeking statewide and legislative office, not those running in local races.

They also promised a full explanation by next week of why they blocked the higher limits. Challengers need that order to seek review by the state Supreme Court.

In the meantime, candidates for the 90 legislative seats are limited to taking only $440 from any one individual or political action committee. Many had already launched fundraising efforts to get contributions up to the now-disallowed higher limit of $4,000 per election.

That includes Senate President Andy Biggs, one of the lawmakers involved in trying to have the appellate court restore the higher limits.

“If you can only raise, max, $440 a pop, you might be able to raise $50,000 or $60,000, or, maybe in the extreme, $75,000 if you have a credible candidate that’s running against you,’’ Biggs said. He said that might fund up to six mailings and some “robocalls’’ to voters.

At the same time, Biggs pointed to the independent expenditure committees that have sprung up in the wake of U.S. Supreme Court rulings that allow them to try to elect or defeat candidates, unfettered by limits on donations or expenditures. If they throw $250,000 into the race, he said, there is no way for a candidate to raise the amount of money necessary.

Liburdi, in his plea Thursday to the appeals court, said candidates like Biggs were suffering “irreparable harm’’ by being limited to those $440 donations.

But Tom Collins, executive director of the Citizens Clean Elections Commission, said that argument misses the point that limits on donations are designed to protect against corruption.

“If I can give you $4,000, the concern is that I’m going to expect a quid pro quo for that,’’ he said.

And he said it’s wrong to believe that allowing donors to give more directly to candidates will result in less money going into independent expenditures.