This is the text of the opening statement that Office of Management and Budget Director David A. Stockman read to a news conference yesterday:

Today at the president's request, I discussed my problem with him. During the meeting, I tendered my resignation. I did so because my poor judgment and loose talk have done him and his program a serious disservice.

Worse, they have spread an impression that is utterly false. President Reagan believes with every ounce of his strength in his program for economic recovery and the better opportunities it will bring to all Americans. Never, ever, has he attempted to mislead the Congress or the American people or to say things which weren't true. To the extent that my quoted words suggest or have been construed to imply otherwise, I take full responsibility and blame.

In our meeting, I told the president that I would not permit my own careless rambling to a reporter to stand in the way of the success of his presidency or the credibility of his program. At the end of the meeting, the president asked me to stay on the team.

But let me be clear on my own account: I would not be here now, nor would I have worked 16 hours per day for nearly a year, if I did not believe in the president and in his policies.

Honest people may worry about how best to advance our vision for getting the messed up economy we inherited back on track and the overgrown budget under control. I have worried, but too publicly, and I deeply regret any harm that has been done.

I am staying on because I believe even more deeply that the president has charted a sound, constructive course. I am grateful to the president for this second chance to get on with the job the American people sent President Reagan here to do.