Christian MP Joyce Chitsulo was in Israel on an Israel Allies Foundation Chairmen's Conference trip.
Jose Tomas Zambrano says Honduras could move its embassy back to Tel Aviv.
Office opening is seen as a partial victory for the campaign to push international recognition of Jerusalem as Israel's capital.
Joint List Mk Tibi wrote to US Secretary of State Blinken in favor of reopening a consulate in the capital that serves the Palestinian Authority.
Only four countries have embassies in Jerusalem, the US, Guatemala, Honduras, and Kosovo, while Equatorial Guinea and Malawi said they would, as well.
The Slovakia mission's move is seen as a victory for Israel’s campaign for recognition of Jerusalem as Israel's capital.
"This embassy is not just a hub for diplomats, but a base to continue in our new partnership."
Honduras is the fourth country to open an embassy in Jerusalem, after the US, Guatemala and Kosovo.
"A truly proud and historic moment for Kosovo-Israel relations," Kosovar Ambassador Ines Demiri tweeted. "The greatest honor of my life is to have this opportunity to open the embassy.
Embassy still in Tel Aviv, but the new mission is an official branch.