Shares of U.S. companies that have bid for foreign companies through so-called inversions came under pressure on Tuesday, after the Obama administration updated rules that sapped some of the tax benefits from these moves.

Medtronic Inc. fell 2.7%, among the top decliners on the S&P 500. The company has agreed to acquire Ireland-based Covidien PLC for $42.9 billion and said it would move its headquarters to Ireland as part of the deal. U.S.-listed shares of Covidien fell 2.4%

Inversions involve a U.S. company buying a foreign rival and relocating the combined headquarters to the lower-tax country. Deals have been concentrated in the pharmaceutical sector, often with a U.S. company acquiring a European one.

The rules don't apply to transactions that have already closed, but they are prompting investors to question whether some deals will have to be renegotiated--or even scuttled.

The Treasury Department is "trying to make inversions a lot more difficult to complete," said Tao Levy, managing director at Wedbush Securities. Mr. Levy covers medical-device companies, including Medtronic.

"Even if it makes a lot of strategic sense .. it might be financially difficult for [the companies] to complete it," said Mr. Levy, referring to the inversion deals.

Shares of Mylan Inc. declined 1.6%. Mylan in July agreed to acquire Abbott Laboratories' overseas generic pharmaceuticals business in an all-stock transaction worth about $5.3 billion. The new company is to be based in the Netherlands. Abbott shares fell 1.1%.

Also coming under pressure were AbbVie Inc. shares, which fell 2.3%. The company agreed to acquire Shire PLC for $54 billion and said it would move its tax headquarters to the U.K.

Write to Saumya Vaishampayan at saumya.vaishampayan@wsj.com

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