Venezuelan opposition leader Juan Guaidó has said he would consider an amnesty for President Nicolás Maduro if he cedes power.
In an interview, Mr Guaidó – who declared himself interim president on Wednesday – said he was reaching out to all sectors including the military to end the crisis.
It comes amid US efforts to block Mr Maduro’s revenue streams.
Mr Maduro has cut ties with the US and has so far been backed by the military.
However the international community is divided on whether to recognise his government.
On Wednesday Mr Guaidó – who is leader of Venezuela’s elected National Congress – said he was the legitimate president.
The US, more than a dozen Latin American countries, as well as Canada and the UK, have backed his claim.
But Russia has condemned foreign support for Mr Guaidó, saying it violated international law and was a “direct path to bloodshed”. China, Mexico and Turkey also back Mr Maduro.
US Secretary of State Mike Pompeo has requested a UN Security Council meeting be held on the issue on Saturday.
At a meeting of the Organization of American States (OAS) on Thursday he described Mr Maduro’s government as “morally bankrupt” and “undemocratic to the core”.
President Trump has said that “all options are on the table” in response to the unrest.
What did Guaidó say?
In an interview with US Spanish-language TV station Univision, he noted that a similar amnesty had played a role in the democratic transition in Chile.
“When the moment comes we will look at it. These amnesties are on the table for all those who are ready to… restore the constitutional order,” he said.
He vowed to hold free elections to “move forward rapidly to overcome this crisis”.
He has previously said articles within the country’s constitution allow him to assume interim power because he believes Mr Maduro’s election, and therefore presidency, is invalid.
Meanwhile US National Security Adviser John Bolton told reporters that the Trump administration was working on a plan to funnel funds to Mr Guaidó.
How did the row develop?
Large protests were organised against, and some in support of, Mr Maduro on Wednesday.
At one demonstration in Caracas, Mr Guaidó declared himself as the country’s interim leader.
Within minutes of his declaration, Mr Trump recognised Mr Guaidó as the country’s legitimate head of state. A number of South American nations, as well as Canada and the UK, have now followed suit.
Mr Maduro has labelled the US comments a “big provocation” and broken off diplomatic relations.
On Thursday, he ordered the closure of Venezuela’s embassy and consulates in the US. However Mr Guaidó has urged Venezuelan diplomats in the US to remain at their posts.
The US state department meanwhile has ordered non-essential staff to leave Venezuela.
A Caracas-based NGO, the Observatory of Social Conflict, says that at least 26 people have been killed in demonstrations so far this week.
What could Mr Trump do next?
Analysis by Natalie Sherman, BBC News Business Reporter
The US has already imposed a raft of sanctions in the past two years, which target officials in the Maduro government, restrict Venezuela’s access to US debt markets and block dealings with those involved in the country’s gold trade.
But so far, the Trump administration has not taken action directly against oil imports, which are a key source of cash.
A stand-off over US embassy personnel could push the White House to take that step.
But analysts cautioned that oil sanctions would likely have limited effect on the Maduro regime, which could redirect shipments to allies such as China and Russia, while blaming the US for any additional hardship.
Why are people protesting?
Mr Maduro has led the country since 2013 and was sworn in for a second term earlier this month. His re-election in May 2018 was marred by an opposition boycott and vote-rigging claims.
The president has faced ongoing criticism international and internal opposition for his human rights record and handling of the economy.
Despite having the world’s largest proven oil reserves, Venezuela’s economy has been in a state of collapse for several years.
Its industry has suffered mismanagement and oil revenue has dropped significantly.
Endemic hyperinflation and shortages of necessities like food and medicine have hit the population hard and caused millions of Venezuelans to flee.
Strategic partners including China and Russia have invested deeply the country’s economy – ploughing billions into trade deals and loans to the help its ailing economy.
Moscow sees Venezuela as one of its closest allies in the region.