Stock prices, which sagged a week ago under a pall of bleak international news, rebounded smartly today as international developments seemed to take a turn for the better.

The Dow Jones industrial average climbed 11.61 today to close at 827.36. The Dow had dropped 7.53 points last week.

But analysts warned that today's climb, as well as last week's decline, cannot be taken as serious indications of where the market is heading. The movements have taken place in relatively light trading, suggesting that managers of big institutions such as mutual funds or pension funds still are sitting on the sidelines.

The New York Stock Exchange opened up and continued in that direction most of the day, although there appeared to be some move to take profits in the last hour of trading. At the 3 p.m. reading, the Dow average was up 13.43. It slipped nearly 2 points by the 4 p.m. close.

Among developments that gladdened investors were:

China's announcement that it was going to pull out of Vietnam.

President Carter's decision to fly to Egypt and Israel this week and Israel's apparent acceptance of peace proposals similar to those made by Carter last week.

Iran's first shipments of oil to the international market since late December, which could temper recent price increases announced by other oil-producing nations within the last few weeks.

Larry Wachtel of Bache Halsey Stuart Shields Inc. said that today's step rise in stock prices in no more convicing than last Tuesday's sharp decline.

"The big money managers are still not convinced that interest rates have peaked," Wachtel said. "They're just sitting back and collecting 10 percent on short-term investments such as Treasury bills."

Until trading volume closes in on 40 million shares a day -- an indication that the institutions are trading in the market again -- prices will fluctuate from day to day but no sustainable trend will develop, analysts said.

"The bears had it last Tuesday (when the Dow fell 14.12 points); the bulls had it today," said one analyst.

Yesterday's 25.7 million shares traded hands compared with 23.1 million on Friday. More than 1,100 stocks rose, while 355 declined on the New York Stock Exchange.

Gambling stocks again were among the most popular issues on both the New York and American exchange. Investors were heartened last week by the New Jersey Casino Control Commission's unanimous decision to grant Resorts International a permanent license to run a gambling casino in Atlantic City.

Resorts stock closed up 3 7/8 on the American to 50 1/4. Golden Nugget, also an Amex stock, closed at 19 1/4, up 1 3/8. On the New York Exchange, Caesars World rose 5 5/8 to 49 1/8, while Bally Manufacturing ended the day at 61 5/8, up 3.

Polaroid, which had lost 11 points in the last seven trading days, gained 2 1/8 of them back today, closing at 40 3/8. Polaroid had some tough going after reporting a disappointing gain in fourth-quarter earnings.

The New York Stock Exchange index of common stocks rose 50 cents to 54.96.

The American Stock Exchange index closed up 1.51 points to 164.49. More than 360 stocks rose while 206 declined.

Analysts said another development that helped push prices higher was the announcement by Bank of New York that it had lowered the interest it charges brokers for loans backed by stocks to 10 3/4 percent from 11 percent. Sometimes, declines in the broker loan rate presage fallls in the closely monitored prime rate, the interest a bank chages its best corporate customers for short-term loans.