Major markets like EU and China often do have a major influence on mergers even though the companies merging could be based in the US and most shareholding could be US.

I think it goes like this: The major market regulator could say directly/indirectly: Hey you can merge in the US ... but good luck operating in our geography in a frictionless manner if we are against your merger. As a regulator we can make life hell for you if you don't obey our anticompetitive laws. Since you derive a high percentage of your revenue/profits you must listen to us !

It all depends on the percentage of sales in the foreign geography. With EU/China it can be quite high -- especially for tech companies.

So yes, foreign powers can and often do block companies from merging.