Speculators lift Qatar's Barwa Real Estate to a month high, helping support the index.
"Institutional traders are on the sidelines, waiting for the next two days," says Hani Girgis, assistant chief dealer at Dlala brokerage.
Index compiler MSCI will announce its verdict late Tuesday on whether Qatar and United Arab Emirates are included in the emerging market index.
Barwa gains 3 percent and most large-caps also edge higher. Qatar National Bank and Qatar Islamic Bank are up 0.07 and 0.4 percent.
The benchmark climbs 0.2 percent to 8,335 points, up in five of past seven sessions.
Meanwhile, Saudi Arabia's index is near-flat, but petrochemicals extend losses after US crude oil fell to a four-month low on Friday.
A dimmer United States economic outlook drove crude to its biggest weekly loss since early May.
“A lot of weakness in Saudi petrochemical names will be mitigated by the temporary solution on the Greek debt situation," says Robert McKinnon, ASAS Capital chief investment officer.
The petrochemical index slips 0.3 percent, with Saudi Kayan Petrochemicals down 0.5 percent and heavyweight Saudi Basic Industries Corp (SABIC) off 0.3 percent.
The main benchmark climbs 0.05 percent to 6,504 points, steadying after declining in the previous three sessions.
Banking stocks support, with heavyweight lenders Al-Rajhi Bank and Samba Financial Group up 0.3 and 0.5 percent respectively.
Trading volumes in Kuwait fall to their lowest in more than two years, with investors concerned about the launch of a new trading platform.
The bourse signed up to implement the Nasdaq OMX trading platform in the first half of 2011, says a Kuwait-based trader says on condition of anonymity.
"Investors are not happy with how the whole process is going and people think the market will tank so you have a day like today with low volumes," the trader says.
Hurdles to implement the new system include annual fees, the need for additional capital and lack of preparation on part of the brokerages, he adds.
Kuwait's index slips 0.4 percent to 6,313 points, down 1 percent in June.
Telecom operator Zain falls 1.9 percent, Kuwait International Bank is down 1.5 percent and contractor Mabanee Company slips 1.1 percent.
Abu Dhabi Commercial Bank helps lift the UAE capital's index after saying it will record a net profit of 1 billion dirhams ($272.3 million) from the sale of its 25 percent stake in Malaysian lender RHB Capital.
ADCB gains 1.9 percent, hitting a 24-month high. It is up 11.9 percent in June.
Abu Dhabi's index climbs 0.5 percent to close at 2,775 points, its highest close since November 2010. Dubai's benchmark slips 0.1 percent to 1,599 points.