"Now they're gonna help us find these people and blow them up, if that's what it takes," Rubio said during a visit to Ecuador.
He also announced the US will designate two of Ecuador's largest criminal gangs, Los Lobos and Los Choneros, as foreign terrorist organisations.
The comments come days after US forces carried out a strike on a boat in the Caribbean Sea. The White House says it killed 11 drug-traffickers, though it did not release their identities.
Late on Thursday, the defence department accused two Venezuelan military aircraft of flying near a US vessel in a "highly provocative move designed to interfere with our counter narco-terror operations". Venezuela is yet to respond to the claim.
Marco Rubio was asked whether smugglers coming from US allies, like Mexico and Ecuador, could face "unilateral execution" from US forces. He said "co-operative governments" would help identify smugglers.
"The president has said he wants to wage war on these groups because they've been waging war on us for 30 years and no-one has responded.
"But there's no need to do that in many cases with the friendly governments, because the friendly governments are going to help us."
The Ecuadorian and Mexican governments have not said they would assist with military strikes.