Money market mutual funds lost another $6.5 billion in assets last week, amid signs that the funds are preparing to fight competition from the new money market deposit accounts offered by banks and savings institutions.

In one month, the funds have lost $21.4 billion, or 9.2 percent of their assets. From a record $232.3 billion on Dec. 1, fund assets dropped to $210.9 billion in the week ending Dec. 29. Meanwhile, sales of mutual funds other than money funds set record sales of $14.9 billion in 1982, up 50 percent from the previous record set in 1980, the Investment Company Institute reported.

Although some of the dollars were withdrawn because of holiday shopping needs and more advantageous rates on government securities, a substantial portion would seem to be going into savings accounts paying above-market promotional rates. No reliable data yet exist on how much money has flowed into savings accounts. However, several survey firms have estimated $20 billion, of which half is from passbook accounts, a quarter from money market funds and the rest from various sources.

The average seven-day yield on the funds declined this week to 8.09 percent from 8.2 percent the previous week, according to Donoghue's Money Fund Report.

The new accounts received a plug this week from Money Fund Safety Ratings publisher Glen King Parker, who recommended his clients abandon the funds temporarily. "The best strategy is to take full advantage of the current bonus rates, and then reassess the situation when those bonuses disappear." Parker urged investors who have sizable sums in so-called government-only funds--which pay a bit less than general funds because they are safer--to switch to higher yielding insured bank accounts, which he rates AA or AAA.

Parker cautions consumers to examine carefully bank and thrift rates based on Donoghue's Money Market Fund Average. Because it is heavily weighted by a large number of low yielding government-only funds and the rate is not compounded, "this enables the banks to claim to be paying more than money funds while actually paying less," Parker said. In his words, a money market account paying half a percentage point more than the Donoghue Average actually yields a half point less than a typical top-performing money market fund. For the week ending Dec. 22, the range of seven-day yields on that index was from 6.8 to 9.2 percent.

Some banks and thrifts are still offering promotional rates in double figures. Riggs National Bank, for example, will guarantee 14 percent for the next week. However, these rates are not expected to be sustained much beyond mid-January.

Meanwhile, money market funds have begun to strike back at their erstwhile victims, using among their methods transfers and private insurance. For example, the Vanguard Group of Valley Forge, Pa., will transfer its customers' dollars to a money market account with the Bradford Trust Co. of Boston. The bank pays the fund a fee.

Similar arrangements have been made by Dean Witter with Allstate Savings and Loan of Glendale, Calif., both of which are owned by Sears, Roebuck. Fidelity Group plans to broker money market accounts for small and medium banks that do not have the expertise to manage the accounts and for individual customers who want the service.

Another tactic is private insurance for money market funds. Prudential-Bache Securities, Shearson/American Express and Kemper Financial Services are all said to be developing insured money market funds. Other funds have responded by reducing their minimum investments to undercut the $2,500 required on the money market account and by reducing the $500 minimum on checks written on the funds.