The money market mutual funds fired the first shot three years ago, using high interest rates to lure depositors' dollars away from banks and savings institutions.

The banks and thrifts finally retaliated this winter with their new, phenomenally successful money market deposit accounts, which not only carried high rates, but were federally insured, as well.

Yesterday marked the beginning of round three and the debut of the first insured money market fund.

The Vanguard Group of Valley Forge announced that St. Paul Fire and Marine Insurance Co. has agreed to provide coverage for its new insured taxable money market fund. One other company, Travelers, also has announced plans to establish such a fund. And the Investment Company Institute, the trade association for mutual funds, has been exploring a group policy.

Meanwhile, figures released yesterday by the Federal Reserve show that the money market deposit accounts still are growing, reaching $298.2 billion from $286.3 billion in the week ending March 2. The Super NOW accounts rose to $24.4 billion, up $1 billion. This week the ICI said money fund assets slipped by $2.2 billion to $187.4 billion.

In the interest-rate competition, the average rate for money market accounts at 50 leading banks and thrifts declined to 8.20 percent last week from 8.38 percent the previous week, according to Bank Rate Monitor. The average rate for money market funds dropped a fraction last week to 7.71 percent, the Donoghue Organization said. And Super NOW accounts averaged 7.09 percent, down from 7.22 percent the prior week, Bank Rate Monitor reported.

Now that interest rates on money funds and money market accounts have come within a whisker--one half of one percentage point--of each other, the competition could become less one-sided. The accounts still hold a yield advantage, but the funds offer better terms. If the money funds add insurance, the two would seem to be neck and neck.

Vanguard's insured fund is expected to yield 7.7 percent initially, or about 40 basis points less than its non-insured fund. (A basis point is one one-hundredth of a percentage point.) Both types require a minimum starting balance of just $1,000 and allow an unlimited number of checks, although the minimum check amount is $250. By contrast, the money market account requires a balance of $2,500 and permits only six transactions a month, three of which can be checks. Moreover, a customer can switch to another of Vanguard's mutual funds without charge three times a year.

Each money account is insured by the federal government up to $100,000. Each new Vanguard money fund participant is insured by a private carrier up to $2 million. From the customer's viewpoint, the insurance prevents the portfolio from going below $1 per share.

The insurance protects the fund against the default of any of the underlying investments.