In its effort to merge with National Airlines, Pan American World Airways has decided to increase its cash offer for every share of National stock from $41 to $50.

The increased bid, contained in an amended merger agreement, brings Pan Am's bid to the same amount offered by Eastern Airlines, which also is seeking control of the Miami-based airline.

L. B. Maytag, chairman of the board and chief Executive officer of National, said supplemental proxy material outlining the amended agreement is being filed with the Securities and Exchange Commission and is expected to be sent shortly to National's shareholders.

National's annual meeting of shareholders, at which a vote on the proposed merger will be taken, is scheduled for May 16 in Miami.

A spokesman for Texas International Airlines, which started the scramble for National last summer, had no immediate comment on the Pan Am move. Texas International has offered $15 cash and $35 principal amount of an 11.75 percent senior sinking fund debenture, due 1989, for each share of National it doesn't already own. The Houston-based carrier and Pan Am each have just under 25 percent of National's shares outstanding.

As of last week, Texas International said it planned to continue to pursue Civil Aeronautics Board approval to gain control over National and to oppose a National-Pan Am combination. The statement followed National's request that Texas International give up and support the Pan Am-National merger if Pan Am raised its offer for the stock from $41 to $50.

Texas International also said at the time, however, that if Pan Am did raises its offer to $50 a share, it would not attempt to vote against or otherwise interfere with the National stockholders' vote on the merger question. On Monday, Texas International asked the CAB for permission to vote its shares; a spokesman for the airline had no further comment on the action. CAB approval is needed because the National shares obtained by the would-be acquirers were placed in separate trusts, which effectively bar their voting in a way that could influence any vote without further CAB action.

National did not trade yesterday pending the announcement of Pan Am's increased offer. It closed the previous day at 38 1/4.