Writing on social media platform X, formerly Twitter, Mr Cohen said he discussed the two nations' commitment to "fighting against terrorism" and "promoting a free trade agreement" with Crown Prince Salman bin Hamad Al Khalifa.
"We look forward to expanding the circle of peace and normalisation to other countries in the region," he said.
The Crown Prince met Mr Cohen at Manama's Gudaibiya Palace, Bahrain state news agency BNA reported.
Prince Al Khalifa said the kingdom holds a "firm stance" towards achieving sustainable peace that guarantees the rights of Palestinians, the report said.
The UAE and Bahrain established ties with Israel under the Abraham Accords, signed in the US in 2020.
Mr Cohen is visiting Bahrain less than two weeks before the third anniversary of the accords.
He was accompanied by a delegation of political and commercial officials and is also scheduled to hold discussions with Bahrain's Foreign Minister Abdullatif Al Zayani.
A video shared by Israeli news outlet Kan showed parts of a ceremony to open the renovated permanent residence of the Israeli Embassy in Manama attended by the Bahraini and Israeli Foreign Ministers.
The new embassy will replace the first one that Israel opened in 2021, a year after it normalised ties with Bahrain.
Mr Al Zayani said the event signified a “shared commitment to strengthening and cultivating bilateral relations”.
“As we build into deeper diplomatic endeavours and engage in bilateral co-operation across various sectors, the establishment of this new embassy assumes a pivotal role in our collaboration,” he said.
Mr Cohen's visit coincides with growing speculation about an agreement to establish ties between Israel and Saudi Arabia.
Israel and the US have said they do not believe such a deal is imminent, while Saudi Arabia has not yet commented on the issue.
The storming of Al Aqsa Mosque compound in Jerusalem and raids by on the Palestinian city of Nablus and the Jenin refugee camp in the occupied West Bank were among the Israeli actions that led to condemnation from the Gulf.
More than 170 Palestinians have been killed by Israeli fire since the start of 2023, according to a tally by the Associated Press.