NEW YORK (AP) _ The nation's basic money supply rose by $600 million in late August, the Federal Reserve Board reported Thursday.

The Fed said M1 rose to a seasonally adjusted average of $688.6 billion in the week ended Aug 25 from a revised $688 billion the previous week. M1 includes cash in circulation, deposits in checking accounts and non-bank travelers checks.

For the latest 13 weeks, M1 averaged $675.1 billion, a 17.9 percent seasonally adjusted annual rate of gain from the previous 13 weeks.

The Fed, in its attempt to provide enough money to stimulate non- inflationary economic growth, has said it would like to see M1 grow in a range of 3 percent to 8 percent from the fourth quarter of 1985 through the final quarter of 1986.