President Bush met his Andean counterparts
Speaking at a joint press conference with Peruvian President Alejandro Toledo in the capital Lima, Mr Bush said that the two nations shared a common perspective on the problem: "We must stop it".
According to the BBC's Peter Greste, the meeting was more about symbolism than substance.
Mr Bush also paid tribute to the progress of Peru's political institutions since his host came to power in succession to Alberto Fujimori.
Historic visit
President Bush arrived in the country on Saturday for talks on regional security, trade and ways to curb drug trafficking.
It is the first visit to Peru by a serving US president.
Only days before Mr Bush's arrival, a car bomb killed nine people near the US embassy in Lima.
"Peruvians have been reminded again this week of the terrible human toll of terror," Mr Bush said, offering his sympathies to the victims.
After his meeting with the Peruvian president, Mr Bush met with other Andean leaders before setting off for El Salvador and the next leg of his tour.
The presidents of Bolivia and Colombia and the vice-president of Ecuador attended the talks - at which discussions centred on a free-trade pact to open US markets to certain Andean goods.
The pact eliminates tariffs on some Andean exports in return for action in combatting drug trafficking.
The region's leaders told Mr Bush that the Andean Trade Preferences Act has been a boon for their economies.
The act expired last year and Mr Bush said he would be pressing for the renewal to be pushed forward through the Senate.
Peace Corp
The president also used his presence in Peru to announce a return of the US Peace Corps to the country after a 27-year absence.
The Peace Corps is an agency that sends American volunteers to help communities outside the US.
"The first volunteers will arrive in August, a symbol of the stronger ties between our people and the stronger relationship between our nations," Mr Bush said.
He also promised increased US aid to support Peru's efforts in stemming a possible resurgence in coca production and heroin poppy crops in remote highland areas.
But no decision was reached on whether to resume drug surveillance flights over Peru - which were suspended after a Peruvian military jet shot down a plane carrying an American missionary family.
Warm welcome
On President Bush's arrival in Lima, he was greeted by trumpeted national anthems, an honour guard and a red carpet as he was met by the Peruvian President Alejandro Toledo at a military base near Lima.
But there was also heightened security following the bomb blast at the US embassy.
No-one has claimed responsibility for Wednesday's explosion and the imprisoned leaders of the country's main rebel groups have denied involvement.