Congress is speeding $6.9 billion in drought assistance toward President Reagan's desk, with Agriculture Secretary Richard Lyng calling on lawmakers to jettison a $300 million benefit for milk producers.

"We strongly object to the provision, which would increase the price support level for milk and urge the House to strike this provision from the bill on the floor," Lyng said Wednesday.In a letter to House Agriculture Committee Chairman E. "Kika" de la Garza, D-Texas, the secretary dismissed dairy industry claims that the price boost is needed to head off a looming milk shortage. And he placed the cost of the increase at $300 million - more than double the House estimate.

"We do not expect milk shortages next year," Lyng said as both the House and Senate prepared to act on their versions of the measure to provide aid to farmers hard hit by the drought.

Farm lawmakers plan to meet in a House-Senate conference committee next week to fashion the final product and send it to Reagan before Aug. 11, when Congress flees Washington's summer heat.

At the core of both versions is a payment program that would provide drought-stricken farmers with compensation equal to 65 percent of crop losses beyond 35 percent of their expected harvest. The plan also would streamline and expand federal feed benefits for dairy and livestock producers.

Under heavy fire from the Reagan administration - and a host of rival farm and business groups - is a House provision that would increase the dairy price support level on Oct. 1 by 50 cents for each 100 pounds of milk to $11.10.

Both bills would cancel a 50-cent cut in the price-support level that otherwise would be automatic under the farm program.

Under the relief bill, payments would be made for losses of a wide variety of crops, including an estimated $150 million for tobacco.

Tobacco-state lawmakers acknowledged that it represented a step away from the 1983 compromise between farm lawmakers and anti-smoking forces under which the tobacco price-support system is supposed to have no net cost to the taxpayer.

In other Capitol Hill action:

- The House Banking Committee ended a grueling 161/2-hour session Thursday by approving a bill described as the most significant change in banking law since the Depression.

If adopted by the full Congress and signed into law by the president, the bill would allow bank holding companies to underwrite virtually every type of security except corporate stock.

However, the legislation includes a laundry list of other provisions banks strongly oppose, including new obligations to serve poor people.

- By a lopsided 361-47 vote, the House approved legislation Wednesday to scrap the 1980 law that groups like the Wilderness Society say is responsible for overharvesting and big Treasury losses in the Tongass forest in Alaska.

The bill moved over to the Senate, where Alaska's two members could have more success in blocking it than its lone representative, Republican Don Young, had in the House.

- The House also gave the Reagan administration a vote of no confidence for its handling of America's national parks. It voted 248-130 Wednesday for legislation to strip political appointees in the Interior Department of their day-to-day power over the National Park Service.

The vote capped nearly eight years of friction over a variety of parks and federal land-use issues between the Republican administration and Democrats on the House Interior Committee.