The meeting on Thursday, a first step toward efforts to arrange an Israeli-Qatari summit, came a day after Qatar's Foreign Minister Sheikh Hamad bin Jassim bin Jabor Al Thani urged Arab nations to open up to the Jewish state.
Sheikh Hamad and Israeli Foreign Minister Silvan Shalom posed for photographs before heading into their meeting in the basement of UN headquarters in New York.
Asaf Shariv, a spokesman for Israeli Prime Minister Ariel Sharon, said Israel is "working now on arranging a meeting with the Emir of Qatar (Sheikh Hamad bin Khalifa Al Thani) and I think that what the (foreign) minister said definitely points to Qatar's trend."
Earlier, on Wednesday, addressing the New York-based Council on Foreign Relations, Qatar's foreign minister said Arab countries should make a gesture towards Israel after its withdrawal from Gaza by talking with their Middle East neighbour to chart a future for the region.
"Arab countries must take a step towards Israel through an international meeting or a meeting between Arab states and Israel and the co-sponsors of peace, particularly the United States, in an attempt to come up with a clear vision to the period after Gaza," Sheikh Hamad said.
The Israeli pullout from Gaza was
praised by Sheikh Hamad
Praising the Israeli pullout after 37 years of occupation in Gaza, Sheikh Hamad bin Jassim said Arab countries should respond, stressing that "it is very important that there be a clear vision after this step".
Sheikh Hamad bin Jassim said the Gaza pullout could bring normalisation of relations with Israel to prominence, but he acknowledged the issue remains "controversial" in the Arab and the Islamic worlds.
The Qatari foreign minister also reminded both Arabs and Israel of their obligations for a post-Gaza Middle East, highlighting the US role to bring the region together after the withdrawal.
"Let them talk together," said Sheikh Hamad bin Jassim , who is in New York to attend the UN General Assembly session.
"If we have to talk to them (the Israelis), it doesn't mean we accept all what they say, but they are part of the United Nations."
He said Arab hardliners were pursuing the "wrong policy" by refusing to talk to Israel.
Qatar, which is a close US ally in the Gulf and host to the US Central Command's forward operations in the Middle East, has had low-level contacts with Israel in the past.
Arabs have proposed a peace plan calling for full Israeli withdrawal from the Gaza Strip, the West Bank and East Jerusalem, where the Palestinians want to establish a state, as well as Syria's Golan Heights.
Shalom: Arab and Islamic states
should open contacts with Israel
In return, Israel will have normal relations and peace with the Arab world.
There is concern among Arabs that Israel will use the withdrawal from Gaza and the dismantling of Jewish settlements there to consolidate its hold on the West Bank.
The Gaza withdrawal prompted countries such as Pakistan, one of the Muslim world's largest countries, to consider establishing diplomatic ties with the Jewish state.
Still, there is an opportunity for the region after the Gaza withdrawal.
At the UN on Wednesday, Israeli Foreign Minister Silvan Shalom urged Arab and Islamic states to open contacts with Israel if they want to help the cause of peace in the Middle East.
He maintained that Israel was making progress on that front but did not divulge the details.
"I think all the Arab and Muslim countries should know that if they would like to help the Palestinians, they should have good contacts with both sides," he said.
"Otherwise, it will be impossible for them to help the Palestinians."