"There is a mutual interest for the three countries in making the world a more secure place," deputy prime minister Lapid told reporters in New Delhi at the end of Israeli leader Ariel Sharon's controversial visit to India.
It was the first ever by an Israeli Prime Minister and was dramatically cut short by Sharon because of growing domestic problems.
"There is American support for the development of this unwritten axis. There is no formal triangular agreement as yet, but in the abstract sense, we are creating such an axis," said Lapid.
He pointed to a recent US State Department statement expressing the hope that Indo-Israeli ties, previously unspoken, would flourish.
Relations between New Delhi and tel Aviv had "improved dramatically", Lapid said, calling it an "open secret" that the two countries were now on an "equal footing as far as the fight against terrorism is concerned".
He warned that internatinal co-operation must be stepped up urgently to fight the terror threat, saying: "Mankind's existence could be threatened the day terrorists lay their hands on nuclear weapons."
He confirmed that prime minister Sharon would curtail his historic visit to India by a day in the wake of Tuesday night's twin suicide bombings in Tel Aviv and Jerusalem.
Sharon will now leave for Israel at 5.30pm local time this evening, cancelling a scheduled trip to India's commercial capital Bombay.
"We are cutting short our visit for the very reason that brought us to India, which is terrorism," said Lapid. "Global terrorism is the most important issue of the 21st century."
Lapid confirmed Israel's readiness to sell three Phalcon airborne early warning systems to India, at a cost of a billion dollars each. The deal would bring much of nuclear armed rival Pakistan's airspace under Indian surveillance.
"There is no obstacle to the sale of the Phalcons as the United States has given its approval," he said.
Israel had agreed to collaborate with India in moves to crack down on international money laundering, sharing its expertise to curb what he termed "a major source for financing terrorists."
Six agreements signed by the two sides to clamp down on drug trafficking and step up ties on the environment and culture represented "stepping stones towards closer and enlarged relations," he said.
An independent Palestinian state would never exist until "Arabs stop terrorising us", he claimed, but argued that heightened Indo-Israeli ties should not be a "disturbing factor" for the Arab world.
"The Indian government has the right to establish relations with any country," he said.
Reacting to the blasts that killed eight at a bus stop outside a military base near Tel Aviv, and a second explosion hours later in a Jerusalem cafe that left seven dead, prime minister Sharon demanded a "full cessation of terror".
Speaking at a banquet hosted in his honour by Indian leader Atal Behari Vajpayee, he added: "In our area we want peace. But due to the terror events in Israel I have to go back today.
"Israel is a small and embattled oasis in a largely hostile region, struggling against brutal terrorism and other gravve threats to its security. Terror is the enemy of freedom and democracy. Israel and India will combat this menace.
It is symbolic that the two nations, which are deeply rooted in history, are working together in peace, which will help ensure a better future for us all."
Prime minister Vajpayee condemned the attacks, saying: "We have repeatedly said we condemn terrorism in all its forms. Violence will not solve the problems confronting the Middle East."
Meanwhile a crank caller sparked a major security alert in New Delhi on Tuesday evening after informing the Taj Mansingh hotel, where Sharon and his delegation are staying, that a group of Palestinian terrorists were about to storm the building.
In a call made shortly after midnight on Tuesday, he warned that a group of Palestinians had infiltrated the Indian capital and planned to carry out suicide attacks at the hotel in a bid to assassinate the Isralei leader.
New Delhi police traced the call to the Greater Kalish district of southern Delhi, and arrested the caller, they claimed. Following interrogations, he was declared to be "mentally unstable".