WASHINGTON (AP) _ President Reagan on Friday signed a bill designed to prevent a threatened cutoff in home mortgage loans guaranteed by the Veterans Administration.

The measure raises the authorized level of VA-backed loans to $18.2 billion, up from $12 billion. Because of spending cuts required by the Gramm- Rudman deficit-reduction law, the amount will be reduced by 4.3 percent.

Faced with Gramm-Rudman cuts, which would have reduced the $12 billion ceiling to $11.6 billion, the VA had said it would have to suspend the home loan guaranty program around April 1.

The problem was compounded by an unexpected increase in demand for loans resulting from falling interest rates.

As Congress signaled its intent to approve legislation on VA's loan ceiling, the agency withdrew plans to suspend the home loan guarantee program.