BRUSSELS—Multinational companies including Intel and Raytheon Technologies are warning that new European Union rules for reporting foreign subsidies are so onerous they could disrupt mergers and acquisitions and impede public tendering. In a letter sent last week to the European Commission, the bloc’s executive body, the companies said the commission “severely underestimates” the work required to comply. The new foreign-subsidy rules, which are set to take effect later this year, will give regulators new tools to bar companies from making certain acquisitions or winning large public contracts if they previously benefited from government aid that the commission believes was distortive.