The diplomatic office in the disputed city, which is scheduled to open on Sunday, will be an extension of Honduras's Tel Aviv-based embassy.
"For me, it's the recognition that Jerusalem is the capital of Israel," Hernandez was quoted as saying on Tuesday.
"This has been much debated in the world and I know that I will be criticised for this, but if Honduras has as capital Tegucigalpa, and another country refuses to recognise it, it is [equivalent to] not recognising our sovereignty."
Hernandez said in March that he would open a trade office in Jerusalem, calling the city "the capital of the state of Israel", but stopping short of announcing plans to move his embassy from Tel Aviv. It was not immediately clear how the diplomatic office would be related to a trade office.
The foreign ministry said in a statement Israel had proposed that Honduras move its embassy to Jerusalem, which is being "analysed and evaluated in the international and national context".
Sara Netanyahu, the wife of Israeli Prime Minister Benjamin Netanyahu, first announced the news about the opening of the office in a Facebook live video on Tuesday.
"I'm happy to announce that on Sunday Honduras is opening a diplomatic mission in Jerusalem, a step on the way to an embassy," she said.
Trump's move plunged relations between Washington and the Palestinian authorities and drew international ire.
Guatemala and Paraguay followed in the US's steps before the latter then reversed its decision after just four months.
During Netanyahu's visit to Brazil last year - the first official trip by an Israeli leader to the country - the prime minister told reporters that the relocation of Brazil's embassy to Jerusalem was a question of "when, not if".
Israel occupied East Jerusalem in the 1967 war and later annexed it in a move never recognised by the international community. The Palestinian Authority views East Jerusalem as the capital of their future state.
Traditionally, most diplomatic missions in Israel have been in Tel Aviv as countries maintained a neutral stance over the status of Jerusalem.