NEW YORK, NOV. 23 -- Stock prices rose slightly in quiet trading today as traders cautiously evaluated plans to narrow the federal budget deficit. The dollar, however, fell.

Trading on the New York Stock Exchange was at its slowest pace in six weeks.

The Dow Jones average of 30 industrials, up 18.24 points on Friday, rose another 9.45 to 1923.08.

Advancing issues outnumbered declining ones by about 9 to 7 on the NYSE. Volume was 143.16 million shares, down from 189.17 million Friday and the lightest total since 141.87 million shares were traded on Oct. 12, when many market participants were taking Columbus Day off.

Analysts said the budget pact announced Friday fell short of what was needed to revive confidence in the financial markets.

But they also said most investors had been aware that progress had been slow in the talks, and thus weren't looking for any big surprises. And they know the agreement still must be approved by the House and Senate.

President Reagan, in separate meetings today with business leaders and Republican activists, described the two-year, multibillion-dollar proposal as a "good, solid beginning" to cut the deficit.

In the meantime, stock brokers said investors might shift focus back to the outlook for interest rates and the impact of last month's stock market collapse on the economy.

Analysts said the dollar fell today in disappointment over the deficit agreement.

The U.S. currency ended in New York at 1.6715 West German marks, down from 1.6740 on Friday. Earlier in Frankfurt, it ended at 1.6667, down from 1.6747 on Friday. The dollar closed in New York at 134.70 Japanese yen, down from Friday's 135.15 close.

In early trading Tuesday in Tokyo, the dollar rose slightly, while the stock market firmed. The markets were closed Monday because of a national holiday.

An announcement of the deficit accord was made Friday afternoon, after many foreign currency markets had closed.

"Most people in the market, including the Europeans, are not enamored with the package," said Bank of Montreal foreign exchange dealer Thomas Benfer. "There's a feeling that it did not address the real budget-cutting questions, such as Social Security."

Earlier, White House spokesman Marlin Fitzwater described overseas reaction to the deficit packageas "supportive and welcomed."

And said Chairman John Phelan of the New York Stock Exchange, one of the 10 businessmen attending at the White House meeting, "This at least sends a message, both domestically, but more importantly abroad, that ... the leadership in this country is willing to sit down and work on the agreement."