The Saudi government had no immediate response to Israeli Energy Minister Yuval Steinitz's remarks. A spokesman for Israeli Prime Minister Benjamin Netanyahu also did not respond immediately to a request to comment.
Both Saudi Arabia and Israel view Iran as a main threat to the Middle East and increased tension between Tehran and Riyadh has fuelled speculation that shared interests may push Saudi Arabia and Israel to work together.
Saudi Arabia maintains that any relations with Israel hinge on Israeli withdrawal from Arab lands captured in the 1967 Middle East war, territory Palestinians seek for a future state.
U.S. President Donald Trump's peace envoys, seeking an Israeli-Palestinian agreement with regional support, have visited Saudi Arabia several times since he took office.
In an interview on Army Radio, Steinitz, a member of Netanyahu's security cabinet, did not characterise the contacts or give details when asked why Israel was "hiding its ties" with Saudi Arabia.
He replied: "We have ties that are indeed partly covert with many Muslim and Arab countries, and usually (we are) the party that is not ashamed.
"It's the other side that is interested in keeping the ties quiet. With us, usually, there is no problem, but we respect the other side's wish, when ties are developing, whether it's with Saudi Arabia or with other Arab countries or other Muslim countries, and there is much more ... (but) we keep it secret."
In an interview with Reuters on Thursday, Saudi Foreign Minister Adel Jubeir, asked about reports of cooperation with Israel, cited a Saudi peace initiative, first adopted in 2002 by the Arab League, as key to forging any relationship.
"We have always said that if the Israeli-Palestinian conflict is resolved on the basis of the Arab peace initiative that Israel would have enjoyed normal relations, economic, political, diplomatic relations with all of the Arab countries, and so until that happens, we don't have relations with Israel," he said.
That plan makes those relations contingent on a full withdrawal by Israel from territory it captured in the 1967 Middle East war, including East Jerusalem.
Netanyahu has expressed tentative support for parts of the initiative, but there are many caveats on the Israeli side.
Hussein Ibish, senior resident scholar at the Arab Gulf States Institute in Washington, said Steinitz's remarks "won't surprise anyone who's been paying attention to the budding courtship between Israel and Saudi Arabia, which is being especially pushed by the Israeli side".
Last week, the Israeli military chief, Lieutenant General Gadi Eizenkot, told an Arabic language online newspaper that Israel was ready to share "intelligence information" with Saudi Arabia, saying their countries had a common interest in standing up to Iran.
Saudi Arabia has ratcheted up pressure on Iran, accusing Tehran of trying to expand its influence in Arab countries, often through proxies including the Lebanese Shi'ite Hezbollah group.
Ibish said that given the mutual threat perceptions shared by Israel and Gulf Arab countries, it is unlikely that covert ties aren't developing.
But he said Israeli officials have tended to exaggerate such interactions in a bid to "drive down the price they may have to pay, especially on Palestinian issues, to expand strategic relations and ties with Arab countries".
In public remarks in September, Netanyahu pointed to covert relationships with Arab states, saying, without mentioning any by name, that cooperation exists "in various ways and different levels".
Also in September, Israel Radio reported that Saudi Crown Prince Mohammed bin Salman had secretly met officials in Israel that month, drawing an official denial from Riyadh.
Last month, Saudi former intelligence chief Prince Turki bin Faisal shared a stage with ex-Israeli Mossad spy agency director Efraim Halevy at a debate on Iran in a New York synagogue.
In 2016, former Saudi general Anwar Eshki visited Israel, where he met Israeli legislators, to promote - as he has at various academic forums - the Saudi peace initiative.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)
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