Salehi and Velasquez made the remarks during a meeting in Tehran on Tuesday.
During the meeting, the Iranian foreign minister pointed to the current status of bilateral ties between Iran and Venezuela, saying, "Tehran-Caracas bilateral relations are deep-rooted and I hope that under the presidency of Mr. Nicolas Maduro we will be able to open a new chapter in our relations."
Salehi said that the relations between the two allies are at their best, and called for an expansion of bilateral cooperation in commerce and industry.
Velasquez, for his part, thanked Iranian officials for their solidarity with the nation and government of the Latin American country.
The Venezuelan deputy foreign minister, heading a high-ranking delegation, arrived in Tehran on Monday to attend the Friends of Syria Conference hosted by Iran.
Last month, Iranian President Mahmoud Ahmadinejad lauded the "strong and growing" relations between Iran and Venezuela, and described Caracas as a major ally of Tehran.
"Venezuela has been a major and loyal ally of the revolutionary nations, including Iran, and it will be so in future as well," President Ahmadinejad said at the time.
Iran has in recent years expanded friendly ties with Latin America, specially in economic, trade and industrial fields.
Since taking office in 2005, Iranian President Mahmoud Ahmadinejad has expanded Iran's cooperation with many Latin American states, including Venezuela, Bolivia, Ecuador and Cuba.
Iran's strong and rapidly growing ties with Latin America, specially with Venezuela, have raised eyebrows in the US and its western allies since Tehran and Latin nations have forged an alliance against the imperialist and colonialist powers and are striving hard to reinvigorate their relations with the other independent countries which pursue a line of policy independent from the US.