"We send our sincere congratulations to the king, government and people of the Kingdom of Saudi Arabia on the occasion of the 93rd national day," the Israeli foreign ministry said in a statement.
"May Allah bring you goodness and blessings, security and prosperity with our wishes for an atmosphere of peace, cooperation and good neighbourliness," it added in the statement on its English and Arabic-language accounts on X, formerly Twitter.
A ministry spokesman told AFP it was the first time such a message had been shared on its English-language account, but that it had been posted in Arabic before.
In an address to the UN General Assembly on Friday, Israeli Prime Minister Benjamin Netanyahu said: "We are at the cusp of... an historic peace between Israel and Saudi Arabia".
Saudi Arabia's de facto ruler, Crown Prince Mohamed bin Salman, had similarly told Fox News that the two counties were getting "closer" to normalising ties.
Several Arab states, including the United Arab Emirates and Bahrain, normalised their relations with Israel in 2020 under the so-called Abraham Accords but Saudi Arabia has so far held out.