National Assembly President Virgilio Saquicela said a commission would be formed to facilitate dialogue to end the strike.
President Lasso suggests that the protesters are seeking to overthrow him from power as he proposed some concessions.
Hundreds of protesters demanding cheaper fuel defy state of emergency, pressing on with road blockages now in their seventh day.
The move followed president’s decision to declare a state of exception in three provinces, in a bid to calm protests called by Indigenous groups rejecting the government’s economic policies.
President Lasso also announced small increase in a monthly subsidy paid to Ecuador's poorest, as well as a program to ease the debt of those who have loans from state-run banks.
Protests will continue until President Lasso solves economic and environmental issues affecting the South American country, Indigenous leader Leonidas Iza says after he is freed from detention.
Latest grisly prison riot in the South American country leaves at least 43 inmates dead while more than 100 others are still at large, officials say.
Rains, landslides have killed 52 people, left more than 100 injured and are affecting more than 27,000 people.
Rain-weakened hillside gives way in Quito, leaving 24 dead, 48 injured and 12 others missing, officials say.
Control of Guayaquil regional prison was regained by police and military after five hours riot that killed nearly 30 inmates, Ecuadorian officials say.
Ecuador President Guillermo Lasso declares a state of emergency in the country's prison system after deadly violence killed at least 22 inmates in jails in southern Guayas province and Cotopaxi province, south of capital Quito.
Under the agreement announced Ecuador President Lenin Moreno will withdraw the International Monetary Fund-backed package known as Decree 883 that included a sharp rise in fuels while the indigenous peoples will end the protests.
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