Venezuelan opposition leader Juan Guaidó has said he would consider an amnesty for President Nicolás Maduro if he cedes power.
Mr Guaidó, who declared himself interim president on Wednesday, said he was reaching out to all sectors including the military to end the crisis.
and vote-rigging claims.
The global community is split on whether to recognise his government.
But so far, Mr Maduro retains the crucial support of Venezuela's military.
Who is backing whom?
The US, more than a dozen Latin American countries, Canada and the UK have backed Mr Guaidó - who is leader of Venezuela's elected National Congress - after he said he was the legitimate president.
But Russia has condemned foreign support for Mr Guaidó, saying it violates international law and is a "direct path to bloodshed". China, Mexico and Turkey also back Maduro.
US Secretary of State Mike Pompeo has requested a UN Security Council meeting on the issue on Saturday.
At a meeting of the Organization of American States (OAS) on Thursday, he described Maduro's government as "morally bankrupt" and "undemocratic to the core".
The Trump administration is working on a plan to funnel funds to Mr Guaidó, who is currently at an undisclosed location.
UN human rights chief Michelle Bachelet raised fears on Friday that the situation "may rapidly spiral out of control, with catastrophic consequences", and called for an independent investigation into claims that Venezuela's security forces used excessive force against protesters this week.
What did Guaidó say?
Guaidó and his allies accuse Maduro of usurping power through a fraudulent election.
"Our challenge is to secure free elections, and we want them as soon as possible. But we are living in a dictatorship," Mr Guaidó told US Spanish-language TV station Univision.
He previously told the Financial Times: "No one wants to live like this, whatever their politics: people going five or six months without running water in their houses, without medicines, without enough money to buy food."
Discussing a possible amnesty for Mr Maduro, Guaidó said a similar move had played a role in Chile's democratic transition.
"These amnesties are on the tab
He has previously said articles within the country's constitution allow him to assume power temporarily because the election was a sham.
How did the row develop?
Large protests were organised against Maduro on Wednesday - as well as some in support of him.
At one demonstration in Caracas, Guaidó declared himself the country's acting president.
Within minutes, Trump recognised Guaidó as Venezuela's legitimate head of state. A number of South American nations, as well as Canada and the UK, followed suit.
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, Guaidó has urged Venezuelan diplomats in the US to remain at their posts.
The US state department 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.