House Republicans offered their solution to the energy problem yesterday, introducing a bill to increase production of oil and natural gas by ending price controls.

The 13 Republicans on the House adhoc committee coordinating the energy bill drafted piecemeal by five legislative committees said their bill would lead to production of an extra 2 million barrels of oil a day - nearly half the savings President Carter hopes for from his proposals. They will try to offer it as a substitute when the House takes up the bill next week.

The Republican proposal would remove federal price controls from all new onshore natural gas. The president would keep controls, but at a higher price.

The Republicans would decontrol new oil over five years. They would keep controls on old oil from wells in operation in 1972, but would force the price up to world levels by a wellhead tax on producers.

Half the tax would be given back to producers if they invested it in exploration for more oil. The rest would go into trust funds to encourage use of mass transit, develop alternative energy sources and help pay for state highway maintenance to compensate for an expected loss of state gasoline tax funds to gasoline conservation.

The President's oil plan would tax oil prices so they reach the world price, leaving free from taxes only "new new oil" produced in the future. The tax would be levied on refiners, not producers, and would be rebated to taxpayers - since its purpose is not revenue-raising but conservation. A proposal to give producers a 20 per cent "plowback" for exploration was rejected by the Ways and Means Committee.

The Republicans retained a gas-guzzler tax on big cars, which Carter proposed, but rejected the 4-cent-a-gallon gasoline tax recommended by the adhoc committee. The Republican bill also retains tax credits for those who insulate their homes and for industries that convert to coal, as in the President's bill.

The Republican bill would exempt all but large boilers - those consuming fuel at a rate of 300 million BTUs or more per hour - from requirements that they convert from oil or gas to coal.

The House rules committee meets Thursday to decide procedures for handling the complex bill on the floor. These are expected to spell out amendments that have been promised a chance for a vote on major issues such as deregulation of natural gas, but they may be prevented from offering their bill except as a final amendment, called a motion to recommit with instructions.

The President's energy bill has made a strong comeback since the day last month when the Ways and Means Committee killed the standby gasoline tax and the rebate for small cars, and when a Commerce subcommittee voted to deregulate natural gas. The full Commerce Committee sided with the president on gas, and most of the rest of the program survived committee action, although there was some cutback in the tax on industrial oil and gas users.

In the Senate, the energy committee plans to report all non-tax parts of the program to the full Senate before the August recess, which begins in two weeks.Finance Committee Chairman Russell B. Long (D-La.) said he plans one week of hearings during the recess, another week after Labor Day, then one or two weeks of markup. That would send it to the Senate floor before the end of September.