Racing against a mid-May deadline for floor action, the House Ways and Means Committee's trade panel yesterday started writing a trade bill that appears likely to toughen existing laws and force the president to retaliate against unfair trade practices by other nations.

The subcommittee markup will continue today and tomorrow and the full committee is scheduled to work on the bill next week. Subcommittee Chairman Sam Gibbons (D-Fla.) said the committee will meet the deadline set by House Speaker Thomas P. O'Neill Jr. (D-Mass.) to bring trade legislation to the floor. To keep the pressure on, committee Chairman Dan Rostenkowski (D-Ill.) attended yesterday's markup.

The Reagan administration has decided not to support any trade bill this year out of concern that it would be highly protectionist. Many provisions of the trade subcommittee's draft bill cut into presidential discretion and broaden the definitions of unfair trade practices so much that the bill might face a presidential veto.

Congressmen from both parties want tough trade laws and a tightening of the president's discretionary powers in unfair trade cases because they feel the Reagan administration has not given enough help to domestic manufacturers hurt by imports.

Rep. William Frenzel (R-Minn.), a longtime free-trader, offered a series of amendments, all defeated, that would have restored presidential prerogatives. "I am giving him the president discretion to do what he considers best," said Frenzel.

But Rostenkowski said that one Frenzel amendment "worries me" because it would bar presidential retaliation until a panel of the international agency that regulates world trade, the General Agreement on Tariffs and Trade (GATT), makes a ruling. "As far as I'm concerned," said Rostenkowski, "the last thing GATT does is make a decision."

The subcommittee quickly tied into the comprehensive bill a provision sponsored by Reps. Robert T. Matsui (D-Calif.) and Judd Gregg (R-N.H.) that would force the government to retaliate against countries that block sales of U.S. telecommunication products.