President Reagan yesterday signed the bill that increases the federal tax on gasoline by a nickel a gallon effective April 1, prompting threats of a nationwide strike by truckers opposed to provisions in the bill that increase federal highway fees for truckers and taxes on new trucks and truck parts.

On Wednesday, before the president signed the bill, White House officials met with a group of independent truckers who support the strike and are still trying to negotiate more favorable applications of the law, such as a cap on state taxes, according to White House spokesman Larry Speakes.

"It was a listening session," Speakes said. "We took their concerns seriously and we'll look into them . . . . We'll work with them, do what we can to assist them. I don't think they were coming in to say they were going to disobey the law, but they raised problems and concerns that they expressed as truckers, and certainly we are sympathetic to their concerns . . . . "

Michael Parkhurst, president of the Independent Truckers Association, said yesterday that 100,000 truckers have committed themselves to strike if the increased taxes on trucks are not rescinded and the federal government does not consider limiting state taxes on trucks.

"The average truck made $40 a month in 1982," said Parkhurst, "and this tax would cost a truck between $300 and $500 more a month. As Mr. Reagan said last night in his Wednesday night news conference , you don't raise taxes in a recession."

Parkhurst would not say when the truckers plan to strike.

Administration officials noted that the the new law also permits heavier, wider trucks to travel on highways as well as increasing taxes on trucks but the independent truckers are not satisfied with the compromise.

In addition to signing the gasoline tax bill, the president yesterday:

Received information from national security affairs adviser William P. Clark on an orbiting Soviet satellite that is expected to crash soon. Speakes said the president is monitoring the situation and has asked that inquiries about the satellite be made of the Soviets through diplomatic channels. American officials believe that part of the satellite's power supply is a nuclear reactor that could cause nuclear contamination on impact.

Held a budget meeting with aides and later met with members of Congress to discuss the budget.

"Decision-making will continue through sometime next week," said Speakes. "We're not going to get into checkoffs on decisions or no decisions. The ultimate decision comes when the president says 'That's it, go with it.' "

Although Reagan portrayed the gasoline tax he signed yesterday as a user fee to benefit motorists by funding the improvement of road surfaces, the $5.5 billion it is expected to raise annually also will fund improvements in mass transit.

The bill provides as much as six additional weeks of unemployment benefits for about 2 million out-of-work Americans who have exhausted their benefits. It also will create about 300,000 jobs, although Reagan has said he is opposed to having the federal government create jobs to lower the nation's 10.8 percent unemployment rate.

"When we first built our highways we paid for them with a gas tax--a highway user fee that charged those of us who benefited most from the system," Reagan said at the bill-signing ceremony that was attended by outgoing Transporation Secretary Drew Lewis, his successor, Elizabeth Hanford Dole, and 17 legislators including Dole's husband, Sen. Robert J. Dole (R-Kan.), who pushed the bill through the Senate.