The world's financial markets reacted cautiously to President Carter's Sunday and Monday speeches in which he sought to re-establish himself as a leader and to outline a new policy to achieve energy independence for the United States.

Markets behaved haphazardly. The dollar declined, as did the prices of bonds and other money market securities. Gold prices rose. So did stock prices - for the first time since last Monday. But in all cases, from foreign exchange trading to stock trading, investors adopted a wait-and-see attitude. Trading was light.

The Dod Jones Industrial Average, the bellwether of the U.S. stock market, closed up 1.37 to 834.90. But with only 26.7 million shares changing hands, volume was the lowest in more than five weeks.

"The main interest was in the coal area," according to E. F. hutton analyst Newton D. Zinder. "The rest of the market behaved rather indifferently. I don't think they (investors) expected too much, so there wasn't any room for disappointment.

While the stock market closed up slightly, the money markets registered lower prices. "While in some cases, the diclines were as much as a half a point, there was a very thin atmosphere, with no retail trading to speak of," according to William Sullivan of the Bank of New York.

Most of what was sold was put on the block by traders seeking to adjust their inventories, and the money markets - for bonds, bills and notes by companies and the government - just "drifted downward," Sullivan said.

On the New York Stock Exchange, 828 stocks closed up in value while 593 closed lower. The 26.7 million shares traded contrasted with a volume of 33.1 million shares Friday.

The most active issue on the NYSE was Congoleum Corp. The company said it had received an offer of $38 a share for its stock Congoleum closed up $7 a share to $32,375 as 388,500 shares changed hands.

The NYSE composite index rose 26 to 58.43 while Standard & Poor's barometer of 500 stocks advanced 41 to 102.74. Overall national composite trading in NYSE issues on all exchanges and over the counter was 30 million shares.

American Stock Exchange prices, as measured by the market value index, rose 1.09 to 197.18. Over-the counter stocks in the NASDAQ index gained .37 to 138.89.