The House yesterday approved, 295 to 85, the first part of President Carter's economic stimulus package, a bill authorizing $4 billion for quick-starting public works projects to create an estimated 600,000 jobs.

The Senate Public Works Committee has approved a bill scheduled for Senate action week after next which authorizes $4 billion for public works, but also provides $1.5 billion for youth jobs and $9 billion for sewage treatment plant construction. After the two houses reconcile differences on the authorizing legislation, the funds must be provided in a separate appropriation bill.

The House is scheduled to act next week on the tax relief part of Carter's package to speed economic recovery.

The public works bill is the second installment of a program enacted last year over President Ford's veto. It provides federal grants covering total costs of public works projects that are ready for immediate construction in areas of high unemployment. Applications must be processed within 60 days, and the projects must be ready to start construction within 90 days.

Last year's appropriation of $2 billion produced 24,000 applications for project grants totaling $25 billion. Only 2,000 could be approved. Work on them is to begin with the spring building season.

The $4 billion in new funds would be handed out for the most worthy of the 22,000 applications still pending. No new applications will be accepted now, said Rep. Robert A. Roe (D-N.J.), manager of the bill.

Most of the five-hour debate was a fight among states over the formula for carving up the money. As reported by the House Public Works Committee, 65 per cent would have been allocated to the states on the basis of the number of unemployed. Thirty-five per cent was set aside for states with unemployment rates above 7.5 per cent.

An attempt to let states with unemployment rates less than 7.5 per cent but more than 6.5 per cent share in the 35-per-cent set-aside funds was rejected, 201 to 187. This is the formula in the Senate bill.

The House then adopted, 229 to 158, an amendment that would allocate all the money on the basis of the number of unemployment rate. Supporters said this would put the money where it is most needed, in pockets of unemployment regardless of a low statewide rate of unemployment.

The House adopted an amendment by Rep. Parren J. Mitchell (D-Md.) which requires that at least 10 per cent of the contracts for materials to build the projects go to minority businesses, if any are available.

Also adopted was a ban on hiring illegal aliens to work on the projects. A Buy-America provision requiring that all materials for the projects be produced or mined in the United States was softened to permit importing needed materials not produced here.