President Carter yesterday signed into law a bill designed to increase competition among the nation's airlines by phasing out federal regulation.

The new law, supported by President Carter since the beginning of his term, gradually reduces the role of the Civil Aeronautics Board in the fare and route decisions of the airlines, and abolishes th CAB altogether at the end of 1984.

Carter said in a crowded signing ceremony in the White House Cabinet Room that the legislation would achieve two critical objective. "One is to help our fight against inflation and the other is to assure American citizens of an opportunity for low priced air transportation," he said.

Thanks to recent actions of the CAB under the leadership of Chairman Alfred E. Kahn, the nation already has seen the beginning of real competition among domestic airlines, Carter said. "Competition has already helped both consumers and the industry," he said. "It brought lower fares, more passengers and higher profits."

Although the airline industry has been subjected to increasing doses of competition in the last few years, supporters of the new law said a bill updating the 1938 regulatory framework was needed to assure a continuation of the benefits that reduced regulation had yeilded.

Supporters of changs in the law feared the move toward more competition could be blunted by a change in CAB members - it had a histroy of protectionism - or through legal challenges to board initiatives that had not yet worked their way through the courts. The new law not only legitimizes what the board has been doing, but goes further and faster than the board could have gone on its own. The law establishes a schedule for elimination of CAB jurisdiction over airline rates, routes and mergers.

"For the first time in decades, we have deregulated a major industry," Carter said, adding later that it set a "sound precedent . . . for dealing with other overregulated industries."

The law eliminates CAB authority over routes at the end of 1981, leaving existing airlines free to start new routes without any application process. New airlines could be formed with a showing that they are "fit, willing and able," the law says.

In the next three years, entry into the industry and into new routes is made signficantly easier than it ever has been. Airlines will be able to pick one new route to enter automatically each of the next three years. In addition, a provision allows airlines almost automatic entry on a first-come, first-served basis to routes going unserved by the airlines holding authority for those routes.

Since last Thursday, representatives of 20 airlines have been standing in line outside the CAB waiting for the chance to apply to those "dormant" routes.The applications will be accepted starting this morning.

Aside from "automatic" entry, routes will be easier to get through the regular application process. In the past, applicants for new routes had to prove they were "required by the public convenience and necessity." Now the burden of proof will be on the opponents of new applications to prove why they are not in the public interest.

Aside form "automatic" entry, routes will be easier to get through the regular application process. In the past, applicants for new routes had to prove they were "required by the public convenience and necessity." Now the burden of proof will be on the opponents of new applications to prove why they are not in the public interest.

At the end of 1982, the CAB will be stipped of its authority over fares and mergers, leaving the airlines subject to the same federal laws that apply to other unregulated industries. In the meantime, the airlines are given the authority to lower their fares by up to 50 percent without CAB approval; they also can raise their fares up to 5 percent unless they carry more than 70 percent of the passenger traffic on a route.