The pro-Russian opposition - which opposes plans to anchor Montenegro in NATO - lashed the announcement of the arrests as propaganda, while Serbia sardonically questioned its timing.
The attacks would have targeted the state and possibly "senior state officials", Montenegro police chief Slavko Stojanovic said in a statement.
The 20 were arrested last night and a 21st individual is being sought, he said.
"They are suspected of coming to Montenegro with the intention of carrying out attacks on institutions, the police and the representatives of the organs of state," the statement said.
Andrija Mandic, head of the Democratic Front, Montenegro's main opposition, immediately condemned the announcement as "gross propaganda."
In neighbouring Serbia, Prime Minister Aleksandar Vucic, quoted by the Serbian news agency Tanjug, said he had no information about the arrests.
"I find it curious that this is happening today, and that's all I'll say," Vucic said. "As for the rest, it would be better for me to bite my tongue."
Campaigning in small ex-Yugoslav Montenegro has been gripped by tension over veteran premier Milo Djukanovic's plans to forge closer ties with the West.
One of the six founding republics of the former Yugoslavia, Montenegro was joined in a loose union with Serbia after the Yugoslav breakup.
The union ended in 2006, when the country narrowly voted in favour of independence, and relations have been fraught ever since.
Djukanovic, 54, is the only Balkan leader to have held on to power since the collapse of Yugoslavia began in the early 1990s, serving several times as prime minister and once as president. But analysts say he is now under pressure, with critics accusing his government of cronyism, corruption and links to organised crime.
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