The brutal selloff in equity and debt markets picked up pace Thursday, fueled by comments from U.S. Federal Reserve Chairwoman Janet Yellen who suggested the yearslong stock rally may have driven prices too high.

The Stoxx Europe 600, was 1.5% lower in Europe midmorning, weighed down by a near 2% fall in some country indexes. In debt markets, the yield on the 10-year German government bond, or Bund, surged to its highest level in more than five months. This yield fell to a record low last month on the back of the European Central Bank's huge quantitative-easing program. Yields rise as bond prices fall.

Stocks also fell across Asia on concerns about the sluggish U.S. economy and overvalued equity markets, following declines for U.S. stocks Wednesday.

The drastic change of direction in markets, triggered by investors turning their backs on some of the most popular trades of 2015, is now into its second week and many who initially dismissed it as a brief correction have started to change their tune.

"This isn't just a market shakeout," said Justin Knight, head of European rates strategy at UBS.

For some weeks Mr. Knight has been saying that bond yields are unsustainable at record low levels. On Thursday, however, he said he was surprised at the sheer speed of the correction.

"Bubbles collapse not because there is necessarily a wave of selling, but because all the potential buyers are already long. That is what's happened here," he added.

The Fed's Ms. Yellen also raised concerns about bond markets in her comments Wednesday, saying that debt investors were taking excessive risks, and by midmorning, German 10-year government bonds yielded 0.73%.

Just over two weeks ago, the 10-year Bund yield hit a record low of 0.05%, spurring predictions of zero or even negative yields on the benchmark for European credit markets. Other government bond yields also rose Thursday.

Bill Eigen, a fund manager at J.P. Morgan Funds said that this is the "most volatile market since the 2013 taper tantrum," when the Federal Reserve indicated it could start reducing its $85 billion-a-month bond-buying program.

"Investors would be wise to focus on stability, reducing the likelihood of capital losses and preserving capital," he said.

In currency markets, meanwhile, the euro continued to climb against the dollar hitting a two-month high early in the session and trading around $1.1372 by late morning, up around 1.5% since the start of May.

The buck rallied hard against the euro during the first few months of the year, largely as a result of the ECB's stimulus measures coupled with expectations that Fed was preparing to raise rates, but that trend has also showed signs of running out of steam.

On Wednesday, U.S. employment survey showed private-sector payrolls once again expanded at a mediocre pace last month, much slower than expected--another sign that the Fed may not raise rates as early as previously expected by the market.

"The longer the Fed waits, the greater the risk of asset price bubbles--and subsequent crashes," strategists at BlackRock wrote in a note.

Elsewhere, the British pound fell around 0.2% to a three-month low against the euro, as polls opened for one of the most closely fought elections in recent U.K. history. Sterling also edged lower against a weak U.S. dollar.

Although the pound has shown resilience in the lead-up to the vote, strategists on Thursday said the currency would likely face headwinds over the coming days, especially if no single party is able to secure a majority, which could lead to lengthy negotiations over a possible coalition.

"If heightened uncertainty weighs more heavily on the pound in the near-term, it could create an attractive opportunity to buy the pound on dips," said Lee Hardman, a strategist at Bank of Tokyo-Mitsubishi UFJ.

London's FTSE 100 index was 1.4% lower in early trade, though strategists said that this was also likely a symptom of the global stock market shakeout, rather than of domestic politics.

The yield on the U.K.'s 10-year gilt was recently at 2.037%. On Wednesday, it surpassed the 2% mark for the first time since December.

Write to Josie Cox at josie.cox@wsj.com

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