President Reagan signed into law today the tax and budget-cutting bills that are the core of his controversial economic program while conceding that budget deficits in the near future may be larger than predicted earlier by the administration.

The president said that present "soft and soggy" economic conditions will continue for several months, but that the tax and budget bills represent a historic turnaround for the United States.

Reagan appeared relaxed and rested one week into his August vacation. He sat at a small table just outside the white stucco house on his beloved California ranch and fielded reporters' questions for about 30 minutes, the usual duration of a presidential news conference.

He strongly defended his decision to produce neutron bombs, claiming that much of the opposition to his action results from an extensive Soviet propaganda campaign.

The Soviets "are squealing like they are sitting on a sharp nail," Reagan said, because the United States is showing that it will not permit Moscow to become militarily dominant "and they don't like that."

On other subjects, the president:

* Defended Interior Secretary James G. Watt as a man doing "a common-sense job in the face of some environmental extremism." He added, "I can assure you Jim Watt does not want to destroy the beauty of America."

* Said he will announce next week his decision whether or not to resume shipment of jet warplanes to Israel and gave some indication he leans toward lifting the suspension that was imposed after Israel bombed a nuclear plant in Iraq.

* Said he will not decide how to base MX missiles or what type of bomber the United States should build until after he returns to Washington Sept. 3.

* Denied that there is any ill-will or feud between Secretary of State Alexander M. Haig Jr. and Secretary of Defense Caspar W. Weinberger.

* Reiterated his willingness to sit down with Soviet President Leonid Brezhnev at an appropriate time, but indicated such a time is not near.

* Declared that he hoped his daughter Maureen will not run for the Senate in California next year.

In an extraordinary setting for a presidential news conference, Reagan talked and joked with reporters until they ran out of questions while a heavy fog on his Santa Ynez mountain retreat about 20 miles north of Santa Barbara limited visibility to about 50 feet.

Reagan said it was the first day of bad weather he's had this week. "I shall refrain from saying that you all are responsible for bringing it up with you," he told the crowd of reporters who were driven to the ranch in vans. It was the first time reporters had been allowed on Reagan's ranch since last August.

Secret Service agents, White House staff members, several horses and two dogs moved through the fog in a field adjacent to the house as Reagan held forth. The president wore a denim jacket, faded blue jeans and brown boots.

At one point he held up his feet to demonstrate that contrary to a statement earlier by deputy press secretary Larry Speakes he is not tucking his jeans into his boots as a precaution against fleas that might be carrying bubonic plague. Health warnings have been posted in the vicinity of Rancho del Cielo since a wood rat that had plague was discovered about a mile away.

The president hailed the Republicans and those Democrats in Congress who worked for the bills that will cut taxes by $749 billion over the next five years and reduce government spending by $130 billion over three years. He used 24 pens to sign the two bills and said the pens would go as souvenirs to "some of those people that helped."

Reagan declined to give a dollar figure for the additional budget cuts that will be required in the next three years to meet his goal of balancing the budget in 1984, but he acknowledged that the deficits in the intervening years may exceed earlier administration predictions.

"Now, the possibility of increased deficits in the coming years over our previous figures are due in part to not getting totally what we had asked for in the budget cuts, but also that the tax package finally came out with additional reductions," the president said.

In the days immediately following the administration's legislative victories on the tax and budget bills, Reagan's top aides said they were satisfied with the bills and would not blame Congress for failing to vote exactly what the White House had proposed.

The president said, "it just means that we are going to have to try to get more additional cuts than we might have had to get before."

On U.S.-Soviet relations, Reagan declared that the neutron bomb is not an American escalation of the arms race, but a countermeasure against the large Soviet advantage in numbers of tanks based in Europe. "The neutron warhead is a defensive weapon," he said.

Twice Reagan took up the theme that most opponents of going forward with the neutron bomb are "really carrying the propaganda ball for the Soviet Union."

Reagan said he does not want a summit with Brezhnev soon, but has suggested in correspondence that "we might sit down sometime and see what it was the people" of both countries "really wanted."

At one point during the news conference, Reagan patted his dog Millie, which had frightened Michael Downing, 3 1/2, son of Newsweek photographer Larry Downing. "She won't hurt you," the president assured Michael, who was watching the news conference.

At the end of the news conference the president and Nancy Reagan took a few moments to talk to Michael, and the president and Michael exchanged salutes. Mrs. Reagan, who watched the news conference, answered one question. When a reporter raised the often-heard theory that while the president loves spending time at the isolated ranch, she is not happy here, she replied:

"I love it." She added: "I really like it up here."