Gold rose as high as $1,518.30 (£918.70) an ounce during morning trading in Europe, before falling back.
Silver briefly reached an all-time high of $49.79 an ounce before retreating to $46.91.
Investors have been buying precious metals as a haven against inflation and recent geopolitical turmoil.
Analysts say gold could even trade even higher.
"We as a company believe that we may see $1,600 an ounce by the end of the year," said Angelos Damaskos, a fund manager at Sector Investments, which specialises in gold and oil investments.
"But gold could easily surprise everybody and go to significantly higher levels because of the relatively small supply of the metal."
Monday was the seventh consecutive trading session that saw the price of gold rise.
The price of gold has risen sixfold in the last 10 years, and has more than doubled since the global financial crisis of 2008.
However, the price of silver has been even more volatile, having quintupled since 2008, and up 12-fold in the last decade.
By mid-morning in London on Monday, silver was trading just below the high of $49.45 that it reached in 1980 following the Iranian revolution and related oil price spike.
'Dollar play'
Much of the rise in both metals is seen as the flipside of a decline in the US dollar.
"It's the dollar play," said a Singapore-based dealer, referring to the gold rally. "There is more room for prices to go even higher."
The greenback has been steadily declining against most other currencies since the end of the financial crisis.
With the US central bank, the Federal Reserve, pumping unprecedented amounts into the financial markets, there are fears the dollar may lose its status as the favourite reserve currency of the world's central banks, with precious metals being an obvious alternative.
On Wednesday, the Fed chairman, Ben Bernanke, is expected to affirm its commitment to quantitative easing, a programme to flood money markets with liquidity.
The policy tends to drive down the value of the US currency, and has been openly criticised by China and other countries who hold large dollar reserves.
The prospect of low interest rates in the US is driving investors seeking higher returns towards gold.
"Investors expect the Fed to continue with low rates, which means the dollar could be even weaker, unless there were game-changing comments from Bernanke," said Ong Yin Ling of Phillip Futures.
Investors continue to react nervously to the uncertainty in the Middle East. An escalation in violence in Yemen and Syria over the weekend has also helped the price of gold strengthen.
Fashion versus utility
However, an equally important driving factor in the rise of gold is its use in jewellery, particularly in India.
Jewellery accounts for more than half of all gold usage, according to the World Gold Council.
And in India, demand for gold jewellery has been skyrocketing, rising 69% last year.
In contrast, silver's rally has been driven by its use in industry, particularly in electronics.
With the global economic recovery, industrial demand for silver rose 21% last year, data from the Silver Institute showed.
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