A smiling President Reagan returned to the White House by helicopter yesterday to a cheering, campaign-style welcome one week after surgery at Bethesda Naval Hospital to remove a cancerous tumor from his colon.

Holding hands with Nancy Reagan, the president walked stiffly across the White House South Lawn while a Marine jazz combo played, "When the Saints Go Marching In." A crowd of 2,000, mostly White House aides and their families, applauded and waved balloons and posters, one of which said, "The Gipper Comes Through -- Again."

"I'm feeling great, but I'm getting a little restless," Reagan said in his weekly radio speech moments before he left the hospital.

The president, who is expected to spend several weeks convalescing in the White House and at his mountaintop ranch northwest of Santa Barbara, Calif., said he was "eager to get back to work."

In the radio speech, delivered from his hospital suite, Reagan lauded his wife, Nancy, the doctors and nurses who had treated him and the American people. Then, turning to business, he criticized the House version of the pending budget bill.

"I hope it gets well soon," Reagan said. "In fact, I told one of the fine surgeons who operated on me that if Congress can't make the spending cuts we need, I'm going to send him up to Capitol Hill to do some real cutting."

White House spokesman Larry Speakes said that Reagan had heavily revised the speech draft, which was given to him Friday. One sentence was a play on words, in which Reagan said he didn't "have as much stomach" for federal spending as he used to, a remark that was greeted by groans when the speech was piped into the White House press room.

Reagan spoke in a voice that Speakes said was "raspy from five days of having a tube down his throat." In one passage of his speech, he presented himself as "Dr. Reagan" and advised members of his radio audience to get a medical checkup "if you think something isn't right."

The president also extolled first ladies of the past, mentioning Abigail Adams, Dolly Madison and Eleanor Roosevelt, and said that "in my book, they've all been heroes." Then he paid an emotional tribute to his wife.

"Nancy Reagan is my everything," the president said. "When I look back on these days, Nancy, I'll remember your radiance and your strength, your support, and for taking part of the business of this nation . . . . Thank you, partner, thanks for everything."

Reagan looked at his wife, who was standing beside him, and winked. He then ad-libbed, "By the way, are you doing anything this evening?"

While Reagan was hospitalized, Nancy Reagan played what officials said was a key role in White House management, conferring daily with chief of staff Donald T. Regan and Vice President Bush and standing in for the president at a diplomatic reception.

Reagan entered the naval hospital July 12 for what was supposed to be the routine removal of a noncancerous polyp from his colon. Instead, a colonoscopic examination detected another growth and the following day surgeons removed a two-inch tumor that later was found to be malignant.

Doctors determined that the cancer had not spread to other parts of the body and said there was better than a 50-50 chance that there will be no recurrence.

The president spent eight nights in his $452-a-day third-floor suite. He receives free medical care as commander-in-chief and also is covered by Medicare and private insurance, officials said.

Speakes said that Reagan will rest today and meet with Regan, Bush and national security affairs adviser Robert C. McFarlane Monday morning. Reagan was expected to rest the remainder of the day, and doctors have said he will not be at full strength for several weeks.

White House officials said he would gradually resume his work schedule and might leave for his annual vacation at the Santa Barbara ranch a few days ahead of his scheduled Aug. 14 depature date. On Tuesday he will greet visiting Chinese President Li Xiannian at an abbreviated arrival ceremony.

Speakes said that Reagan probably will lobby members of Congress by telephone on the deadlocked budget bill this week and may meet with congressmen "just to catch up on a number of items that are on the agenda."

Reagan began yesterday with a breakfast of granola, banana, skimmed milk and whole-wheat toast. He met with doctors, who pronounced him fit to go home, and did some last-minute editing of his weekly radio speech, his first public words since the operation.

At 12:16 p.m. a band from the Washington Naval District struck up "Anchors Aweigh" and the Reagans, holding hands, emerged from the 20-story hospital where hundreds of white-garbed Navy men and women flanked the entrance. Reagan thanked the medical team and saluted the naval personnel, who applauded. One young Navy woman burst into tears.

Officials said that Reagan wanted to get home as quickly as possible, and doctors permitted him to return by helicopter. Originally, a motorcade was scheduled so that Reagan's healing incision would not be subjected to the vibrations of a helicopter ride.

When the president's helicopter alighted on the South Lawn, hundreds of spectators gathered outside the White House for a glimpse. He and Nancy Reagan descended, stopped to pet their dog, Lucky, and then walked on a red carpet into the diplomatic entrance of the White House where they were greeted by nine cabinet members led by Secretary of State George P. Shultz. The welcoming party included Senate Majority Leader Robert J. Dole (R-Kan.) and his wife, Transportation Secretary Elizabeth Hanford Dole.

While Reagan was hospitalized, Sen. Dole was critical of the White House on budget issues, though he directed most of his fire at Regan.

The Reagans, still holding hands, appeared on the South Portico, where the crowd cheered them again and released its balloons. As the band continued to play, Reagan turned to his wife and said, "Shall we dance?"