The government would use “all its powers” and the armed forces if necessary, Deputy PM Bulent Arinc said on state-run television.
It is the first time the Islamist-rooted ruling party has raised the prospect of deploying the armed forces.
The issue is sensitive as the army is seen as a bastion of secularism.
PM Recep Tayyip Erdogan told hundreds of thousands of supporters at a rally in Istanbul on Sunday that the protesters were manipulated by “terrorists”.
Trade unions have called a strike to protest against the police crackdown on demonstrators which has seen some 500 people arrested.
Medical officials estimate that 5,000 people have been injured and at least four killed in the unrest.
The protests began on 28 May against a plan to redevelop Istanbul’s Gezi Park, on the city’s central Taksim Square, but it snowballed into nationwide anti-government protests after the perceived high-handed response of the authorities under their three-term prime minister.
Bulent Arinc told state-run TV that “the innocent demonstrations that began 20 days ago” had “completely ended”.
Any further demonstrations would be “immediately suppressed”, he added.
“Our police, our security forces are doing their jobs,” he said.
“If it’s not enough then the gendarmes will do their jobs. If that’s not enough… we could even use elements of the Turkish armed forces.”
The deployment of gendarmes – a military unit under control of the interior ministry in peacetime – shocked some protesters in Istanbul this weekend.
In a separate interview, Interior Minister Muammer Guler stressed that he had not called on the army to help police the protests.
But he argued that the use of the gendarmerie was “quite normal”, the Turkish newspaper Hurriyet reports.
Bloggers reacted with skepticism to news that the army might be deployed.
“And this coming from the same people who always claim they liberated Turkish democracy from army intervention,” one wrote.
In Turkey’s capital, Ankara, riot police could be seen facing off with trade union activists on Monday.
Police officers used megaphones to order workers to stop their march towards the central Kizilay district, reports Reuters news agency.
“Those of you on the streets must stop blocking the streets,” they said.
“Do not be provoked. The police will use force.”
Union marches were also being planned for Istanbul, where police evicted protesters from their camp in Gezi Park over the weekend.
The Confederation of Public Workers’ Unions (KESK) and Confederation of Progressive Trade Unions (DISK), along with three professional organizations, announced a one-day work stoppage to demand an end to “police violence”.
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