Mr Cossio said the onus was now on Mr Morales to make concessions
Bolivia's government has begun talks with a key opposition leader after days of clashes between supporters and opponents of President Evo Morales.
Government officials are meeting Mario Cossio, the governor of Tarija region, to try to ease tension in energy-rich eastern areas held by the opposition.
The talks come after 30 people were killed in the region of Pando.
The crisis centres on Mr Morales' decision to hold a referendum on a new constitution in December.
The president says he wants to re-distribute Bolivia's wealth and give a greater voice to the large indigenous community.
Opposition leaders oppose the plan and demand greater autonomy as well as more control over revenues of natural gas in their areas.
The talks between government officials and Mr Cossio are being held at the presidential palace in La Paz.
Mr Morales is determined to push through with constitutional changes
Before the meeting, Mr Cossio said the onus was now on President Morales to make concessions so that further violence could be averted.
Earlier, one of the opposition leaders has ordered the lifting of his supporters' widespread roadblocks in Santa Cruz province, which have left the energy-rich area short of gas, oil and food.
Branko Marinkovic said the move was a "sign of good will" which could foster dialogue and prevent any more blood being spilled.
In a separate development, the military on Sunday re-took control of Pando's provincial capital, Cobija, two days after the government declared a state of emergency there.
Defence Minister Walker San Miguel said a relative calm had been restored to Cobija.
US envoy expelled
The troops also continued to find bodies from a "massacre" of pro-government farm workers on Thursday, in which officials said nearly 30 people were killed.
On Saturday, President Morales ordered the arrest of Pando Governor Leopoldo Fernandez for allegedly orchestrating the attack, saying he had hired "Brazilian and Peruvian assassins" to carry out the "ambush".
Mr Fernandez has denied having anything to do with the deaths, insisting they were the result of clashes between rival groups.
The ongoing crisis will be the focus of an emergency regional summit on Monday.
Chilean President Michelle Bachelet said she hoped the Union of South American Nations (Unasur) could help promote a democratic solution.
"We cannot be idle in the face of the situation, provoking anxiety among us," she said.
The Bolivian crisis escalated when Mr Morales expelled the US ambassador to La Paz, Philip Goldberg, accusing him of stoking anti-government sentiment.
Mr Goldberg has rejected the accusations, saying the expulsion was a grave error.