Rep. John Rhodes (R-Ariz.) announced yesterday he will quit his post as minority leader at the end of next year, but said he will run for reelection to the House.

The announcement immediately started a battle between Republican Whip Robert Michel (Ill.) and Republican Congressional Campaign Committee Chairman Guy Vander Jagt (Mich.) for the job. And it set off a scramble among five conservative Republicans for the whip spot Michel is vacating.

Rhodes, 63, said he was giving up the leadership post as a "matter of personal preference. This is a tough job." Rhodes took over the job in 1973, when then minority leader Gerald Ford was appointed vice president to repladce Spiro Agnew.

Rhodes listed the frustration of being a leader of Republicans at a time when the Watergate backlash reduced Republicans to about one-third of the total membership of the House, and the frustration of having too few members to get Republican initiatives enacted.

He also has been under pressure from a hard-charging class of 37 freshman Republicans. They have been critical of Rhodes' leadership, calling him too passive and low-key in talking on the Democrats. By last summer, their disillusionment amounted to "near insurrection," as one member put it.

Rhodes has taken steps to quell the criticism this fall and was considering running again for minority leader. But he was told by Michel and others he would have to fight off challengers to keep the post.

"I didn't want him blind-sided like Charlie Halleck was," Michel said. Helleck lost the leadership spot to Gerald Ford through a coup that was kept virtually secret until the last minute.

If Republicans picked up the 58 seats needed to make them the majority party he would run for speaker, Rhodes said. "Other than that, I can't think of anything nicer than being an elder statesman in my party."

Rhodes said he had considered retiring from the House altogether, but pressure from his home district, where a battle to succeed him threatened the loss of the seat to the Democrats, changed his mind.

Rhodes said there was only one condition under which he would consider running again for minority leader -- "if a bloody battle harmful to the party developed and I could head it off." Rhodes said his position was similar to former president Ford's in the current presidential race. Ford has said he would not run unless his party demanded it.

But both Michel and Vander Jagt quickly said that possibility would not arise.

Michel, 56, has been the party head-counter since Rhodes became leader. He is considered an adept stragegist and willing to mind the nitty-gritty details of floor work.

Vander Jagt, 48, had been an aggressive campaign chairman, raising the committee's election funds from $900,00 a year when he took over to $10 million a year now. He is known as a dynamic orator, but he has spent little time on the floor.

His position as campaign chairman has given him more contact with newer Republicans in the House who are often grateful for the campaign funding he doles out.

Vander Jagt said he would campaign on a platform of "who can best transform our minority into a majority." As campaign chairman, he will also have a leg with the next class of freshman Republicans, most of whom he will meet in his campaigning around the country.

Michel, on the other hand, starts with a broad base of support."My feeling is it is primarily the role of the leader to be out there on the floor," Michel said. Sources said freshmen once bedazzled by Vander Jadt's style have come to appreciate the value of the sometimes plodding work Michel has done.

"It will be a show horse against a work horse," one Republican said. "There's not a dime's worth of difference in their philosophies."

This is also true of the scramble among the five Republicans who want to be whip. They are all in the party's conservative wing, which has grown considerably in the last four years. Only about 20 of the House's 159 Republicans could now be put in the moderate to liberal category.

The five are: Republican Policy Committee chairman Bud Shuster (Pa.), Trent Lott (Miss.), Henry Hyde (Ill.), John Myers (Ind.) and Robert Bauman (Md.).

It is too early to predict a winner in that goup. Hyde has led successful fights against federal funding of abortions, and came within two votes of being elected conference chairman this spring.Bauman, a leader of the right, is a master of parliamentary maneuvers and a watchdog of floor action. Shuster has led the fights to balance the federal budget. Lott serves on the Rules Committee, and Myers has been an active deputy whip.