The Marines tried yesterday to secure a beachhead for their oft-crashed Harrier airplane in President Carter's new budget by calling it "our No. 1 priority."

Defense secretary Harold Brown has tentatively pushed the advanced Harrier out of the corp's proposed budget in the belief that a simpler and cheaper plane could do the job of supporting Marine ground forces.

The corps. said Lt. Gen. Thomas H. Miller Jr., chief of Marine aviation, has concluded that most battles are decided "in about 30 minutes" and that the Harrier can reach the battle faster than other aircraft.

The British-designed Harrier would be deployed in rough fields near the front lines so it could come to the aid of ground troops in a hurry, strafing and bombing the enemy. The plane does not need a paved runway. It can take off and land vertically.

But the Harrier has experienced one crash after another in the hands of Marine pilots.

Of the 110 Harriers the corps has purchased, 26 have crashed by the Marines' official count. Miller told a Pentagon press conference yesterday that 20 of those crashes were the fault of the pilot, not the plane.

Miller said training in the most difficult phases of Harrier flying will be increased from 17 to 31 hours as part of the effort to reduce the accident rate.

Also Miller said, the corps is cutting new flying orders for Harrier pilots forbidding them from flying lower than 200 feet in the daytime and 1,000 feet at night. There were no previous restrictions, he said.

The Navy, which purchases the planes for the Marines, sent a budget proposal to Brown recommending buying a total of 90 advanced AV-8B Harriers through fiscal 1983. Those 90 planes - 12 in fiscal 1981, 24 in fiscal 1982 and 54 in fiscal 1983 - would be the first part of a total order of 350.

Brown has recommended that instead of starting to buy the advanced Harrier in fiscal 1981 the corps settle for buying more A-4M Skyhawks for troop support.

"Budget negotiations are not complete." Miller said yesterday in declaring the corps is still fighting for the advanced Harrier. If Brown and Carter reject the advanced Harrier. Miller said, the corps would regard more A-4M Skyhawks strictly as a bridge to buying an attack version of the F-18 fighters now under development.