In the statement the presidents of nine South American countries expressed their "full and firm support for the constitutional government of President Evo Morales, whose mandate was ratified by a big majority".
The statement was agreed by Morales and the presidents of Argentina, Brazil, Chile, Colombia, Ecuador, Paraguay, Uruguay and Venezuela.
Cristina Kirchner, Argentina's president, said after the six hours of talks that "the agreement was unanimous".
The leaders also said they were looking at creating a committee to attend talks between Morales's government and rebel governors in Bolivia's east who oppose his rule and are seeking autonomy for their states.
|Fernandez was arrested in connection with the deaths in Pando [AFP]
They encouraged both sides to negotiate an end to Bolivia's political crisis, which has disrupted natural gas supplies to Argentina and Brazil.
At least 18 people died and 100 were wounded in Bolivia's northern state of Pando last week after clashes broke out between government supporters and opponents.
The South American leaders condemned the deaths in Pando and called for a commission to investigate allegations that many of the victims were pro-Morales peasants shot dead in an ambush.
Morales' government has said it will charge the rebellious eastern governor with genocide for allegedly ordering the killing of peasants, a part of Bolivian society that strongly supports him.
On arrival in Santiago, Chile's capital, Morales accused his enemies at home of mounting a "civic coup d'etat".
The summit statement said the presidents "warn that our respective government energetically reject and will not recognise any situation that attempts a civil coup and the rupture of institutional order ... which could compromise the territorial integrity of the Republic of Bolivia".
"We hope opposition groups can understand this statement as being from all of South America, not just its presidents," Morales said after the summit.
The violence in Bolivia has also sparked a diplomatic standoff between Bolivia and Venezuela on the one side, and the US on the other, with Morales and Hugo Chavez, the Venezuelan president, expelling Washington's ambassadors to their countries, accusing them of backing the opposition.
Washington responded by ordering the Bolivian and Venezuelan envoys to the US to leave.