President Reagan said last night he is "very distressed" by the controversy over lobbying of his administration by former White House deputy chief of staff Michael K. Deaver and declared that he has the "utmost faith" in Deaver's integrity.

"Mike has never put the arm on me or sought anything or any influence from me since he has been out of government," Reagan said in response to a question at his nationally televised news conference.

The president, recalling his long relationship with Deaver, said the former White House aide has been criticized "because he's being darned successful and deservedly so."

Deaver recently has attracted attention as a highly visible and well-paid lobbyist for several corporations and foreign governments seeking to influence the administration.

The General Accounting Office is investigating Deaver's actions as a White House aide on the acid rain issue and his subsequent hiring by Canada as a lobbyist on acid rain and other issues. Deaver also recently lobbied the budget director on the B1 bomber issue, despite rules that restrict lobbying by former officials of the agency where they worked in government. Deaver has denied wrongdoing in both cases.

Questioned about other lobbyists who represent foreign governments at odds with the United States, such as Angola, Reagan at first shrugged it off as "private enterprise." But he added that these lobbyists "don't become my favorite person if they do that. And I wonder sometimes what their motives are or whether they fully appreciate the nature of their client. But there is no way that I think that we should suddenly raise their taxes or something."

Also yesterday, Senate Judiciary Chairman Strom Thurmond (R-S.C.) announced that he plans to introduce legislation placing new restrictions on lobbying by former government officials.

Asked about sharp declines in oil prices, Reagan defended Vice President Bush, who last week stirred controversy when he called for "stability" in the oil market to protect U.S. producers. Reagan, like Bush, stressed two distinctly different themes: That market forces should be allowed to work, but also that the national security would be threatened if U.S. producers are hurt too badly.

"I can't find myself quarreling with any of the remarks he's made," Reagan said of Bush, who has come under political attack in some areas for appearing to advocate higher gasoline and home heating oil prices.

On other topics last night, Reagan insisted that his forthcoming summit with Soviet leader Mikhail Gorbachev not interfere with the midterm election season. Reagan acknowledged that it is getting late to hold the meeting in June, as he had originally hoped, but said July was still possible, and if not then, "after the election." Some White House aides had originally favored the election period for a summit, but others, including Chief of Staff Donald T. Regan, felt the pressures on Reagan's time would be too strong.

Reagan brushed aside the harsh rhetoric Gorbachev used in a speech this week to describe U.S.-Soviet relations since the Geneva summit. "He must have been reading Pravda and Tass too much," Reagan said. "Why don't we send him some American newspapers?"

Departing Soviet Ambassador Anatoliy Dobrynin this week brought Reagan a letter from Gorbachev expressing a desire for continued dialogue. Reagan noted last night that Gorbachev's private communications to him have "certainly been in the spirit of Geneva" as well as his responses to Gorbachev.

Reagan expressed a desire for "sizable and realistic gains in lessening the tensions" at the next summit, language similar to that used recently by Gorbachev, who has called for "concrete" agreements to come out of the meeting.

The president defended his decision to order a reduction in the size of the Soviet delegation to the United Nations, saying some members were engaged in "extracurricular activities that were not for our benefit."

In response to another question, Reagan said he had not decided whether to abide by the limits of the SALT II treaty. Next month, the United States is scheduled to begin sea trials of a new Trident submarine, and Reagan must decide whether to dismantle two Poseidon submarines to remain within the limits of the treaty.

Reagan opened his news conference with another call for Congress to vote his $100 million aid package to the rebels fighting the Sandinista government of Nicaragua, stressing bipartisanship and the need to pressure the Sandinistas into negotiations by providing arms to the "freedom fighters."

He also expressed desire to fund a fourth space shuttle orbiter to replace Challenger, which exploded in flight Jan. 28, but said he had not yet seen the final proposal. "I would hope that we could continue this," he said, "This was the request from every one of the families of those people who lost their lives on the Challenger -- that we continue this program."