Rouhani, winding up a two-day visit to Oman, said the Islamic republic offered "a hand of fraternity to all the countries of the region."
"Relations with one country should not grow at the expense of another. We want to see the countries of the region live in peace, understanding and friendship," Rouhani told a business gathering in Muscat.
The sultanate maintains strong links with Iran and has played an important role as mediator between Western countries and Tehran.
Its Arab neighbours have expressed concern about the reliability of Iran's sole nuclear power plant at Bushehr in the southern Gulf and the risk of radioactive leaks should it be hit by a major earthquake.
Like world powers, they also fear a possible military dimension to Iran's nuclear drive, despite repeated assertions by Tehran that its atomic ambitions are peaceful.
Ties between Gulf countries and Iran have also been strained by Tehran's backing of Syrian President Bashar al-Assad's regime in its battle against rebels supported by the Arab monarchies.
"Cooperation and rapprochement would benefit the whole region," said Rouhani, adding that his country is "open to investors from the region, especially Omanis."
Oman and Iran are seeking to expand trade, which reached $1 billion last year, and bilateral investments which they expect will top $10 billion by the end of this year, Iranian Ambassador Ali Akbar Sibeveih said Monday.
Oil- and gas-rich Iran has been struggling to export its products due to strict US and European sanctions on Tehran over its controversial nuclear programme.
Iran and Oman signed a preliminary agreement Wednesday to build a $1 billion, 200-kilometre (125-mile) submarine pipeline to import gas from the Islamic republic.
- Dialogue against terrorism: Rouhani -
In a meeting with university professors, Rouhani denounced "terrorism" and called for dialogue to coordinate the fight against it.
"All differences can be resolved through dialogue," he said, pointing out that talks had helped end the deadlock in Iran's nuclear negotiations with Western countries.
"Our message to the other countries of the Persian Gulf is a message of friendship, fraternity and cooperation," Zarif said.
" Iran is ready for strong and fraternal relations with all the states of the region," said Zarif, who has embarked on a charm offensive towards the Gulf since Rouhani became Iran's president in August.
In December, he toured Kuwait, Oman, Qatar and the UAE.
But Zarif has still not visited regional heavyweight SaudiArabia or Bahrain, which accuses Tehran of fomenting opposition among its Shiite-majority population.
Zarif has said he is ready to visit Riyadh, but the Saudis remain cool to the idea.
Relations between Iran and Sunni-ruled Saudi Arabia have long been strained as both countries vie for regional dominance.
In a joint statement issued at the end of Rouhani's visit, the president and Oman's ruler, Sultan Qaboos, "stressed on the need to implement cooperation programmes and develop relations on all levels."
The sultanate hosted secret talks between Tehran and Washington ahead of the signing in Geneva last November of a breakthrough interim accord between world powers and Iran on its nuclear programme.