WASHINGTON (AP) _ The first step in bailing out Texas' largest bank holding company is raising concerns about the long-term health of the fund that insures deposits in most of the nation's commercial banks.

The Federal Deposit Insurance Corp. said Thursday it was loaning $1 billion to banks owned by First RepublicBank Corp. of Dallas for six months in a move to reassure depositors worried about the banks' shaky real estate loans.

The infusion represents only about 5 percent of the FDIC's insurance fund, which backs deposits of $100,000 and less at 13,600 banks. But bank analysts believe it could turn out to be the first big hit of a bad year for the fund.

FDIC Chairman L. William Seidman isn't saying how much he believes his agency ultimately may have to spend to rescue the $33.2 billion holding company, the largest in Texas and the 13th biggest in the country.

The analysts, however, are suggesting that the First RepublicBank loan is, in effect, a down payment on a $2 billion to $4 billion problem.

First RepublicBank is about the same size that Continental Illinois Corp. was in 1984 when it required the largest-ever government bank bailout of $4.5 billion.

And more bad news is likely from other banks, particularly in Texas, where Mcorp, a $21 billion, money-losing bank holding company, has been exploring restructuring options.

But Seidman says the situations of Continental and First RepublicBank are not the same and he points with hope to FDIC conversations with private investors and to signs that Texas' economy is rebounding.

He notes his fund's survival during 1987, the worst year for commercial banking since the Great Depression, both in terms of low profits and the number of bank failures.

Despite the rescue of First City Bancorporation of Houston and the failure of 184 banks in 1987, the FDIC fund still managed a modest increase to $18.3 billion.

''Therefore, we don't see anything that we are going to do this year that is going to cause a substantial decline in the fund. I mean by substantial, 25 percent,'' he said.

However, Bert Ely, an Alexandria, Va., financial consultant, said, ''My sense is they are going to lose money.''

The fund's income from interest and from premiums paid by member banks - $3.3 billion last year - is increasing at a slower rate than deposits, he said. The ratio of FDIC assets to insured deposits has fallen from more than $1.20 per $100 in 1981 to close to $1.10.

Still, the FDIC fund is in far better shape than its sister fund for the thrift industry, the Federal Savings and Loan Insurance Corp. Unlike FSLIC, the FDIC probably would still be in the black after accounting for all of the problems suffered by its member institutions, Ely said.

Industry experts are skeptical of the chances for FDIC's efforts to attract private investors to take on some of the risks of operating a restructured First RepublicBank.

''I'm sure there probably are people who are kicking the tires and have expressed an interest to the FDIC,'' said Stephen Skaggs, a senior analyst for Sheshunoff & Co., an Austin, Texas, consulting firm.

''But I just don't see that there's any great appetite for investments (like First RepublicBank) unless the FDIC is willing to assume substantially all of the risk.''

According to Sandy Flannigan, an analyst with Paine Webber Inc. in Houston, the search for private capital for First RepublicBank does not improve the chances for other Texas banks such as Mcorp to attract new investors.

First City, which is getting $500 million from a private investment group in addition to the FDIC money, ''was first to the well,'' she said. ''They are in far better shape than those who follow. There isn't an infinite number of investors interested in Texas banks.''

Ironically, the deepening bank crisis comes amid signs that Texas' economy is improving.

''The whole thing is just a very sad situation,'' said Paul Getman, senior financial economist of The Wefa Group, a Philadelphia-area consulting firm. ''Just when people thought the situation in Texas might turn around, it has in fact worsened. ... The overall economic situation ... has picked up a bit, it has just not improved fast enough to help these banks. ... It's just too little too late.''

''The scary thing ... is that if right now these banks are doing so poorly with an economy that is doing fairly well nationally, what will happen to them if the national growth turns sluggish for the next few years?'' he asked.