The Congressional Budget Office reported yesterday that its preliminary calculations show President Reagan's budget has underestimated defense spending by $14.7 billion for next year, and the chairman of the House Budget Committee asked Reagan to resubmit his budget.

Chairman William H. Gray III (D-Pa.) said in a letter to the president that the defense estimates in the fiscal 1987 budget are "unrealistic" and thus do not meet the $144 billion deficit target in the new balanced-budget law.

A key part of that legislation was struck down by a federal appeals court yesterday, but the deficit targets are expected to remain as political if not legal goals.

Office of Management and Budget Director James C. Miller III said in an interview yesterday that "we think our estimates are very reasonable." Miller said he is "troubled" by criticism from Congress that the defense estimates are too low, noting that estimates made in the congressional budget resolution last summer were $5 billion lower.

But Miller also said that "if we become convinced" the congressional criticism is valid after studying it, "we probably would submit some additional sources of savings." The administration's budget proposed $38 billion in deficit savings for next year, but officials had earlier been prepared to seek more if necessary.

At issue is the amount of defense outlays, or spending, for fiscal 1987, which begins Oct. 1. Reagan's budget estimates that outlays will increase 6 percent, to $282 billion, next year. But given recent experience, some analysts on Capitol Hill and elsewhere have challenged this as too low.

These estimates are difficult to make because spending for weapons is often spread over several years, even though Congress may have provided budget authority, or appropriations, for the weapon in one year. Sudden changes in the rate of spending can result in significant changes in these estimates; in recent years, the administration's estimates tended to be too high. Another factor was a congressional compromise last summer, in which the House estimate of outlays was matched with a Senate figure on budget authority. The compromise may have understated outlays for a given level of budget authority, and this was then carried into the new budget.

The dispute is important because the balanced-budget law requires Reagan and Congress to meet deficit targets leading to a balanced budget by fiscal 1991. Failure to meet the targets could trigger much deeper cuts in defense and domestic spending.

Reagan submitted a budget with a $143.6 billion deficit, saying that he reached the target. But if defense spending has been underestimated, the target would not have been reached.

CBO Director Rudolph G. Penner said in a letter to Gray released yesterday that based on the budget authority requested in Reagan's budget, the spending for next year would be $296.9 billion, or $14.7 billion over the White House estimate. For the current year, Penner said the CBO estimates spending of $269.4 billion, or $3.6 billion over the Reagan estimate.

Gray said to Reagan, "I do not feel that we can proceed effectively. . . given the unrealistic defense outlay estimates in your budget proposal."

Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) has also said the defense estimates may be $10 billion to $15 billion to low, but he has not called on Reagan to revise the budget.