President Reagan yesterday called the nation's environmental programs "the strongest in the world" and stoutly defended Interior Secretary James G. Watt's record in designating federal wilderness areas and maintaining national parks.

In his weekly nationwide radio address, the president said from Camp David, Md., that it is "time to clear the air and straighten the record . . . . I believe in a sound, strong environmental policy that protects the health of our people, and wise stewardship of our nation's natural resources."

The president has recently moved to adjust and defend his positions on a number of issues other than the economic, budgetary and foreign policy questions that tended to preoccupy him during his first 30 months in office. Education and civil rights are two of the areas where Reagan has sought to soften his image; the environment is a third. And Reagan's choice of the environment as the topic of his radio speech seemed to be a part of this.

The president made only passing reference to the Environmental Protection Agency, the main environmental trouble spot for the administration this year. Instead, he concentrated on Interior Department programs and did not mention what has lately become the most prominent issue there, Watt's program of leasing coal rights on federal lands.

But Reagan has consistently defended Watt's efforts to increase development of federal lands and did so again yesterday on the wilderness issue. Watt has recommended that 800,000 acres of federally owned land be removed from consideration as possible wilderness areas.

"What was the firestorm all about?" Reagan asked rhetorically.

He said that the Carter administration rejected 150 million acres for wilderness designation and asked, "Do you recall hearing one word about this or any attack being made on anyone at the time?" Further, he said, his administration has recommended the addition of 57 wilderness areas encompassing a total of 2.7 million acres.

Environmentalists who say they are concerned that the action on the 800,000 acres is a prelude to similar actions on more than 20 million acres still under review have sued.

Rafe Pomerance of Friends of the Earth said yesterday that "Ronald Reagan was telling us a fairy tale today, not describing his environmental record. His administration has been consistently anti-wilderness, anti-parks and anti-wild rivers . . . . "

Watt also has moved to correct deficiencies in the national park services, Reagan said. When Watt came to Washington, Reagan said, "Jim found that visitor facilities in our national parks had been allowed to deteriorate to the point that many failed to meet standards for health and safety."

An early draft of Reagan's speech defended Watt's coal-leasing policy, but the reference was not part of his delivered remarks. Late last week, Carl Bagge, president of the National Coal Association, said that he was concerned that presidential involvement might politicize the situation.

The Senate is scheduled to vote Tuesday on a House-passed proposal that would ban virtually all coal leasing until Oct 1.

Rep. Barbara B. Kennelly (D-Conn.), in the Democratic response to Reagan's speech, said that, in defending Watt, Reagan "is beginning to sound like the fond father of a consistently delinquent child." Most of Kennelly's speech attacked Reagan's refusal to support a limit on the income tax reduction scheduled to take effect July 1.