The world wide rush for gold pushed prices above $700 an ounce today following indications the United States government may not sell any more gold until the market stabilizes.

In New York, the price of gold finished at $712.50 higher than its Monday close. Less than two weeks ago it passed the $600 barrier and less than three weeks ago topped $500 an ounce for the first time.

Silver closed up $3.80 an ounce, to a record $46.30, and other precious metals climbed as well.

The dollar, meanwhile, which traditionally declines when the price of gold rises, finished higher against both European currencies and the Japanese yen. The dollar was added by rumors circulating in foreign currency market that Iran might release the hostages as a conciliatory gesture to the U.S., presumably because of the massing of Soviet troops near the Afghanistan-Iran border.

Analysts said most of the demand for gold continues to come from anxious Middle Eastern investors, worried about the safety and stability of their governments in the wake of the Soviet invasion of Afghanistan and the continued turmoil in Iran.

The Nicholas Deak, president of the gold trading from Deak-Perera, also said there is renewed buying from nervous Europeans, especially in those countries bordering the Soviet bloc.

As headlines blare new record gold prices each day, increasing numbers of Americans are buying the metal as well, although analysts say the bulk of the demand still seems to be coming from the Middle East.

The price of gold takes only small -- and infrequent -- downturns because few investors are interested in selling it, despite the big profits many of them might make.

"The Arabs want the gold as protection. They've got enough money to buy almost anything that comes on the market of any price," said one New York trader. Analysts assume that Middle East investors are working through agents such as West Germany's Dresdner Bank or Switzerland's Credit Suisse.

The price of gold finished at about $684 an ounce in London, then hit $700 in early New York trading before falling back to about $685 around midday.

But the price here surged again after Tresury Secretary G. William Miller said that U.S. government does not think it appropriate to sell some of its gold in an "unsettled and uncharacteristic" marketplace.

U.S. gold sales have been adding to the available supply of the metal, although nearly ever ounce auctioned has been snatched up by West German or Swiss banks, probably acting as agents for Middle Eastern interests.

Miller said the gold prices are the result of world tension and said there is no way to predict where prices will head.

A few minutes earlier Federal Reserve Board member Henry Wallich called the escalation of gold prices a "side show" that does not require any action by world governments. Wallich, the Fed's international expert, said in an interview with Dow Jones News Service that there is no need to halt gold sales either to aid the U.S. balance or to protect the dollar against speculation.

Until October, the Treasury has been holding regular monthly auctions of its gold and the International Monetary Fund holds regular auctions as well.

Even though the rumor of a rapprochement between Iran and the United States that sent the dollar shooting up could not be confirmed, the U.S. currency ended the European trading day sharply higher.

It closed at 1,7280 marks, up from Frankfurt's Monday close of 1.7190. The dollar was worth 1.5930 Swiss francs, compared with 1.5817 on Monday.

The British pound, which soared to $2.2807 on Monday, fell back to $2.2760 today. In Japan, where the dollar closed at 236.17 yen Monday, the U.S. currency could buy 239.5 yen today.