Occidental Petroleum is offering the Ecuador government up to $1bn (£569m) in disputed taxes, investments and extra revenues to end a legal dispute.
Anti-American feeling has risen in Ecuador
The row centres on whether the US firm transferred part of an Ecuadorean field to Canada's EnCana in 2000 without approval from the Ecuador authorities.
Occidental proposes giving Ecuador at least $600m in extra revenues from the disputed area, but denies wrongdoing.
The company faces the possibility of having its Ecuador licence revoked.
It currently extracts 100,000 barrels per day from the country, South America's fifth largest oil producer.
Occidental's offer also includes $100m for health and social development projects.
It has further pledged to invest $110m in new projects with Ecuador's state oil firm Petroecuador.
In addition it will pay a $50m bonus for contract changes and $13m towards the Energy Ministry's plans to modernise its tax system.
Ecuador's Energy Ministry is continuing to look at the Occidental case.
Occidental has been caught up in recent anti-American protests in Ecuador.
Indigenous groups blocked highways last week to demand the government in capital Quito ends free trade pact talks with the US and kicks Occidental out of the country.