The statue of conquistador Gonzalo Jimenez de Quesada was pulled down as tensions simmered in the capital, with hundreds of people march through the streets.
Demonstrations began last week, fuelled by outrage at a plan to raise sales taxes.
That proposal was cancelled but protesters' demands now include a basic income and the withdrawal of a long-debated health reform that opponents say is too vague to correct inequalities.
Accusations of heavy-handed police repression has also fuelled further criticism of the government.
The human rights ombudsman has reported 26 people killed since protests began. Advocacy group Human Rights Watch has reports of 36 deaths and called police violence "alarming."
In the rural area of Cajica, protesters blocked streets to express anger towards the government. Duque denounced the blockades and called for dialogue.