The White House yesterday countermanded Interior Secretary James Watt's ban on rock music at Fourth of July festivities on the Mall, and President Reagan awarded Watt a plaster foot with a hole in it for what Watt called "shootin' yourself in the foot."

Watt appeared on the White House lawn carrying the foot and said, "I've learned about the Beach Boys in the last 12 hours. And we'll look forward to having them in Washington to entertain us again."

In Canada, Elliot Lott, the group's tour manager, said the band has not talked directly to officials here about a July 4 concert, but "I think we will probably go." Lott also said Nancy Reagan telephoned the Beach Boys before their appearance in Fredericton, New Brunswick, last night. "We were very surprised to hear from her and it was great," he said.

White House spokesman Anson Franklin telephoned a reporter last night with the administration's "final word" on the matter: "The president has no objection to the Beach Boys appearing on the Mall this Fourth of July."

Deputy Press Secretary Larry Speakes said earlier at a press briefing that the group will "be welcome on the Mall." Beach Boys member Michael Love said, if logistics could be worked out, a combined Beach Boys/Wayne Newton show "fully representative of American music" might be possible. Las Vegas singer Newton, a millionaire Reagan supporter, is scheduled as the main event as things stand now.

The uproar over Watt's ban continued yesterday among the public and within the highest ranks of political power.

Watt's reason for the ban, given in an interview with The Washington Post, had been that rock groups attracted "the wrong element" and encouraged drug abuse and alcoholism. Watt had said he wanted "patriotic, family-based entertainment" and had arranged for Newton and the U.S. Army Blues Band to provide it.

Yesterday on the White House lawn, Watt said, "The president is a fan of the Beach Boys . . . and I'm sure when I get to meet them I'll like them . . . We need to express patriotism in America and the Beach Boys can--will--help bring us patriotism, I'm sure."

The president summoned Watt to the Oval Office for the foot "award" yesterday morning after the first lady telephoned the Interior secretary to say her children grew up with the music of the Beach Boys and that "they are fine, outstanding people and that there should be no intention to indicate that they cause problems."

In Congress, Rep. George Miller (D-Calif.) took the floor for a one-minute speech that incorporated more than a few Beach Boys lyrics: "Mr. Watt, do you remember those good vibrations from the Fourth of July when all we did was dance, dance, dance all summer long to the Beach Boys in the spirit of America . . . these California girls, they get around and they are not going to back down because they are true to their school and they are going to shut you down like a 409 on graduation day . . ."

The two musical parties involved managed kind words for each other yesterday. "The Beach Boys are great friends of ours," said Newton spokesman Alan Margulies, pointing out that Beach Boy Al Jardine and Newton are both in the Arabian horse-breeding business. Love, on tour with the Beach Boys in Canada, added, "We have nothing against Wayne Newton, he's a great entertainer of his style of performing. He's a total professional, a great performer and a responsible, upstanding citizen of the United States of America and all that."

Love confirmed reports of a barrage of concert offers, including one from Sen. Robert Dole (R-Kan.), who offered to be a go-between for a Fourth of July charity concert in his home state "now that the group seems to be available. I'll admit I am not a pop critic, but I know from the unsolicited comments of my staff that the Beach Boys are not hazardous to your health."

Love said the Beach Boys had not yet received any formal notice from the National Park Service, which falls under Watt's authority and which runs the Fourth of July festivities, or the White House about an appearance on the Mall this July.

"Our calendar is clear," Love said. "We hold off every year to do something special. Meanwhile, we're accumulating invitations." Love mentioned that a major brewery is interested in supporting the Beach Boys for four shows on the Fourth, with the group flying into different cities, including Washington. "We'd like to do something spectacular. It's a way of promoting good times and good spirits . . . good vibrations," Love said.

NBC News reported yesterday that Budweiser was offering to organize a four-city tour, but that the Washington concert would not be on the Mall.

The Beach Boys are already scheduled to perform here June 12 in RFK Stadium before the opening game of Washington's new soccer team, Team America. Newton is scheduled to appear May 19 at a $1,000-a-seat Kennedy Center benefit in the 500-seat Terrace Theater, a center spokesman said. His performance will be followed by a dinner-dance.

The Beach Boys drew hundreds of thousands of people to Fourth celebrations on the Mall in 1980 and 1981. The Grass Roots, another pop rock group, did the same last year.

There is still some question as to who is picking up the expenses for the July 4 concert, which Newton manager Margulies said would probably be televised. "Mr. Newton is coming in totally at his own expense," said Margulies, "including bringing his Arabian horse for the parade ." Douglas Baldwin, Watt's press secretary, said it was his understanding that Newton would be paying for staging, sound, lights, sanitation, security and insurance, costs that have approached $100,000 in previous years.

However, Jerry Harvey of National Independence Day Festival and Parade Inc. said his organization was "working with a major corporation, hoping they will be willing to help pay for that."

Harvey's group also is planning the first National Choir Festival, which will include a sunrise flag-raising ceremony at the Reflecting Pool "with all the choirs singing patriotic music," and Efrem Zimbalist Jr. reading the Declaration of Independence. "We hope that's the spark that will light up the spirit of patriotism and make it a good day when everybody's proud to be an American and waves the flag and hurrah for America and apple pie and motherhood," Harvey said.

Alan Burns, manager at radio station Q107, which had sponsored the first three holiday pop concerts and had applied for a 1983 permit last July 8, said Q107 had met with Harvey's group and Park Service officials several times since September without being informed that Newton was a candidate for the concert.

"From a list of 30 artists we'd run by the Park Service," Burns said, "we narrowed it down to five who we felt were very good possibilities for the date: James Taylor, Linda Ronstadt, Billy Joel, John Denver and America. . . . The first we heard of Wayne Newton was a couple of weeks ago."