Chemical New York Corp., the holding company for Chemical Bank, upped the ante yesterday in its bid to acquire Florida National Banks of Florida.

An increase in the floor offer from $38 to $42 a share to all Florida National stockholders was made in an effort to thwart Southeast Banking Corp., which is engaged in a hostile attempt to take over Florida National.

Chemical seeks to acquire a substantial interest in Florida National in preparation for the day when the prohibitions against interstate banking are lifted and the New York giant can break into the lucrative Florida market.

Last November, Chemical and Florida National announced that Chemical would pay shareholders 1 1/2 times the book value of Florida National common stock at the time of acquisition, or $38, whichever price is higher.

Southeast tried unsuccessfully once before to acquire Florida National, the state's fourth-largest bank holding company. Florida National objects to a union with Southeast because it does not want to be swallowed up by a Florida rival.

Southeast, which questions the legality of Chemical's bid, sought to block it this week by acquiring an option to buy 32 1/2 percent of Florida National stock, which is held by a Venezuelan concern. Southeast offered C.A. Cavendes Sociedad Financiera, an investment company that owns South American banks, $36 a share for its stock, or $86.4 million. The offers would go up to $40 a share if Florida National abandoned its own attempt to acquire another company, thus diluting its stock.

Southeast officials said late yesterday they were still studying the situation.

In related news, the Federal Home Loan Bank Board this week announced two more supervisory mergers of troubled savings and loan associations, the fifth and sixth such moves this year. By comparison, there were a total of 23 in all of 1981. Four of the mergers have involved large, strong California institutions taking over smaller, troubled ones in the East and Midwest.

California Federal of Los Angeles, one of the largest S&Ls in the country, will acquire United Federal Savings and Loan of Broward County, Fla., and three Georgia S&Ls: United Federal of Odel, Peach State Federal of Bremen, and First Federal of Sylvania. That brings Cal Fed's assets to $8.4 million. Some federal assistance was paid Cal Fed for taking over Peach State, the bank board said.

On Thursday it merged Central Illinois Building, Loan and Homestead Association of Clinton, Ill., with assets of $30 million, into Mutual Home and Savings Association of Decatur, Ill, with assets of $225 million.

Yesterday savings institutions testified before Senate subcommittees on a bill to bail out thrifts by allowing wealthy investors to buy low yielding mortgages and get a tax deduction for the difference between the par value and market rate.