DONETSK, Ukraine — Around the south and east of Ukraine, in vital cities in the country’s industrial heartland, ethnic Russians have staged demonstrations and stormed buildings demanding a wider invasion of their country by Moscow.

But some of the people here calling for Russian intervention are themselves Russian — “protest tourists” from across the border.

They have included passport-carrying Russians, like Aleksey Khudyakov, a pro-Kremlin Muscovite who said he traveled here “to watch and maybe to give some advice.” In Kharkiv, another Russian scaled a government building to dramatically plant his country’s flag — offering at least the image that President Vladimir V. Putin’s forces were being invited in.

It is clear that in this part of Ukraine, many ethnic Russians distrust the fledgling government, and some would indeed welcome Russian troops. But the events unfolding in major Ukrainian cities in recent days appear to match a pattern played by the Kremlin in Crimea, where pro-Moscow forces paving the way for Russia to seize control were neither altogether spontaneous, nor entirely local.