Duque had been neck and neck in polls with the leftist former Mayor of Bogota Gustavo Petro, but Sunday's results make him the favorite to be the nation's next president, according to Alvaro Forero, a political analyst at Bogota's Leadership and Democracy Foundation.
Colombian President Juan Manuel Santos has said peace talks with the rebel National Liberation Army (ELN) will resume after a six-week halt.
Meanwhile, the hardline Democratic Centre party - founded by former president Álvaro Uribe and fiercely critical of the peace deal - won 15.89%, the largest share.
Petro's promise of a "social economy" that would raise taxes and shift away from oil, Colombia's top export, towards agriculture has anxious investors in the Andean nation as opinion polls showed the former member of the disbanded M-19 guerrilla group and ex-mayor of Bogota running ahead of Duque. Colombians vote in the first round on May 27 with a likely runoff in June.
Finally, Almagro reiterated the unbreakable commitment of the hemispheric organization to continue to accompany social and institutional efforts to build peace through the Mission to Support the Peace Process (MAPP/OAS), which is celebrating 14 years of uninterrupted work in the most isolated territories and those most affected by armed violence in Colombia.
Petro won the day's other primary with 2.8 million votes, or 85 percent.
Sunday's primaries - in which Duque won nearly 42 percent more votes than Petro did - were considered a better test of voter support than often inaccurate opinion polls, although some voters will have participated strategically and may not back either victor in the presidential vote.
The elections mark the debut of the former FARC rebels as a political party.
"The FARC are in a tough spot", said Leon Valencia, a former combatant who now runs the Peace and Reconciliation Foundation, a think tank.
The FARC is guaranteed five seats in both the 108-member Senate and the 172-member lower house under the terms of the accord.
Petro said that despite the fact that right wing parties performed better in the legislative elections, his newly formed party has a good opportunity to win the presidential ones.
Duque and Vargas Lleras, from the Radical Change party, have strong party machines behind them and can count on backing in Congress if they win.
Two candidates under pressure to join forces are Humberto de la Calle, who was the government's chief peace negotiator, and former Gov. Sergio Fajardo.