President Carter's chief anti-inflation advisor warned yesterday that consumer food prices will rise sharply for the remainder of the year.

Alfred Kahn told a news conference that increases in the food price index would be about 1 percent a month for the next several months. Kahn said food prices rose 5.9 percent in the 12 months to June, but will rise at an annual rate of nearly 12 percent in the months ahead. He predicted the overall rise in food prices will be about 9 percent for the year.

Kahn also predicted that the nation's underlying rate of inflation for the year will be between 9 percent and 9.5 percent. Although this was basically in keeping with earlier Carter administration forecasts, other White House advisers privately predicted this week that the underlying rate of inflation will be closer to 8.5 percent to 9 percent because of unexpectedly moderate wage behavior in recent months.

Kahn said mortgage interest rates were a bright spot in the consumer price picture. These exaggerated boosts in the index earlier in the year and now will be holding down the overall price rise. Federal mortgage officials predicted yesterday that mortgage interest rates may have peaked at their current 14 percent level.

In another economic development yesterday, the Commerce Department reported that manufacturers' orders for durable goods increased 8.1 percent in September, due in large part to heavy spending for military vehicles.

The 5.8 billion increase, to a seasonally adjusted $77.2 billion, followed a revised decline of 3.5 percent in August.

Shipments of durable goods during the month were up 4.8 percent to $75.3 billion after an 0.7 percent decline in August. The backlog of unfilled orders rose 0.7 percent to $273.5 billion following a drop of 0.2 percent last month.

That report said $3.7 billion of the increase in orders was for transportation equipment, up 27 percent over August to $17 billion. In turn, defense orders were responsible for more than 75 percent of the gain in transportation equipment.

The brightest spot in their report was a continued rise in orders received by the primary-metals industries. Four big monthly increases, including 8.2 percent in September, have pushed the value of these orders to within $1.2 billion of the record high of $13.5 billion recorded in Janury before the recession began.

The figures are not adjusted for price increases.

Durable goods, which account for about 17 percent of the nation's total goods and services, are those expected to last for three years or longer. They include cars, household appliances, industrial machinery and defense hardware.

Orders for durable goods dropped an average of 0.1 percent a month during the past 12 months and fell steadily from February through June as the recession took hold. But orders turned around in July and increased by 11.3 percent -- the biggest gain in 6 1/2 years.

In August, as most other government statistics were indicating an end to the recession, orders fell by a revised 3.5 percent. More than three-quarters of the drop was blamed on a decline in orders for aircraft, an industry that only the month before had shown an 18 percent increase in orders.

The Commerce Department said orders for machinery were up 1.7 percent in September to $24.1 billion.

The increase in shipments last month brought the total for the third quarter to $219.4 billion compared with $210.7 billion in the second quarter and $233 billion in the first.