By Tommy Stubbington 

European shares tumbled to their lowest in a week Tuesday, rattled by the latest sign that the eurozone economy is stagnating.

Further adding to the gloom, new rules from the U.S. Treasury Department designed to deter firms from using overseas acquisitions to cut their tax bill dented shares in the health-care sector. Shire and AstraZeneca, which have been subject to takeover interest from U.S. companies, both fell more than 5% after the move to slow the wave of so-called inversion deals.

The Stoxx Europe 600 index was 1.3% lower midway through the session, deepening Monday's decline.

The fall came after data firm Markit's monthly composite purchasing managers index--a measure of activity in the manufacturing and services sectors in the currency bloc--for September fell to 52.3 from 52.5. The figure was the lowest level in 2014 to date. A reading below 50.0 indicates activity is declining, while a reading above that level indicates it is increasing.

The weak data and setback for Europe's prospects for takeovers are a "perfect combination" to put stocks under pressure, according to François Savary, who oversees around $10 billion of assets as chief investment officer at Swiss bank Reyl.

"If you can't count on M&A activity then you have to look back at fundamentals. Today's data shows the recovery will be only gradual which will have an impact on people's earnings expectations," he said.

The eurozone data are likely to put further pressure on the European Central Bank to come up with fresh stimulus measures to prop up the flagging recovery. ECB President Mario Draghi signaled Monday that the central bank remains open to a program of quantitative easing if inflation stays too low.

"If there's too much bad news the prospect of more from the ECB isn't enough to hold up markets. We already had a lot of QE optimism in the price," said Christian Stocker, an equity analyst at UniCredit.

France continued to lag behind other economies in the region, with data there pointing to a deepening slump in business activity.

French shares led declines, with the CAC 40 down 1.9%. Germany's DAX fell 1.3%.

U.S. stocks were poised to extend Monday's decline, with futures pointing to a 0.4% opening loss for the S&P 500. Changes in futures aren't necessarily reflected in market moves after the opening bell.

The latest disappointment for the eurozone overshadowed a positive lead from Asian markets, where shares rallied after better-than-expected Chinese manufacturing data. Worries about slowing growth in China had been behind Monday's declines, which were led by mining stocks as metals prices took a pummeling.

Mining firms outperformed the wider market Tuesday, with the Stoxx Europe 600 basic resources falling just 0.1%.

"Although the data offer some near-term relief, China's growth concerns are likely to continue to weigh the markets," said analysts at Barclays.

The Australian dollar also staged a modest comeback, rising 0.4% to $0.891 after tumbling to a seven-month low on Monday, pressured by the slump in commodity prices.

In corporate news, shares in Austrian bank Raiffeisen tumbled after it issued a profit warning due primarily to the Ukraine crisis.

U.K. food ingredients manufacturer Tate & Lyle also fell sharply after saying profit for the year will be lower than previously expected.

Write to Tommy Stubbington at tommy.stubbington@wsj.com

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