Gold and silver prices today continued the steady, fast climb that began a week and a half ago.

Although analyst said that part of the recent rise can be attributed to renewed interest on the part of Middle Eastern investors, they said no particular event has triggered the price climb. "Nothing really has happened. Everything I can cite was true three weeks ago. It's basically a change in market perception," said James Sinclair, president of Sinclair & Co., a metals trading firm.

Gold closed at $624 an ounce in New York today, up $17.50 from its final Friday price on the Commodity Exchange. Silver prices jumped $1.08 an ounce to $17.88.

In the last seven trading days, gold has climbed about $110 an ounce, while silver has risen $5 an ounce.

The dollar closed lower in calm trading today, in large part because of the continuing decline of U.S. interest rates. The dollar had been strong for the first four months of the year because high interest rates here convinced foreign investors to put their money in U.S. securities.

But since interest rates began their steep descent in mid-April, the dollar has declined as well. As usual, when the dollar declines, gold prices rise, although the spurt in gold prices took place more than six weeks after the dollar began to slide.

In late 1979 and early this year, precious-metals prices soared, in part because of political instability in the Middle East and in part because of speculative mania fueled by the Hunt brothers of Dallas and their Middle Eastern partners, who invested heavily in silver.

But gold and silver prices peaked in January and fell steadily until late March. The decline in silver was so abrupt that the Hunts ran out of money to pay their silver speculating debts and nearly triggered a financial panic in late March.

"There's no mania like that today. It might sound stupid, but the only intelligent thing to say is that metals prices moved sideways long enough," said one trader.

After hitting bottom at the end of March, gold and silver prices moved in a narrow trading range until late May, when they began to climb. Gold, which closed above $900 an ounce at one point in January, traded at between $500 and $525 an ounce for most of the last two months.

Silver, which once touched $50 an ounce during heavy speculation in January, traded in the $12 to $14 range after hitting as low as $10.80 on March 27, the day the Hunt's inability to pay their debts became public.

Sinclair said that investors have begun to look at a number of factors in a different light than three weeks ago, which accounts for the renewed buying interest in precious metals:

The willingness of U.S. officials "to lessen their dedication" to the fight against inflation as the economy continues to deteriorate.

The continuing struggle between President Carter and his chief challenger for the Democratic nomination, Sen. Edward M. Kennedy (D-Mass.). Sinclair said many investors are convinced that Kennedy's challenge will force Carter to take economic positions he otherwise would not.

Anxiety among many investors in Europe and the Middle East because of the willingness of many European leaders to "appease Soviet aggression."

The entry to the United States Treasury into the sale of gold medallions.

"This upgraded gold in people's consciousness again."