The Kuwaiti index climbed 0.4 percent. Many investors hope index compiler FTSE will decide at the end of this month to upgrade Kuwait to secondary emerging market status, which would bring fresh inflows of passive funds.
Blue chips that would be targets of such funds rose on Tuesday, with logistics giant Agility gaining 1.7 percent.
A Reuters poll of leading Middle East fund managers, published last week, found 62 percent expected to raise their allocations to Kuwaiti stocks over the next three months and none anticipated cutting them, partly because of the FTSE hopes.
Abu Dhabi's index edged down 0.1 percent but Dana Gas , the most heavily traded stock, surged 5.5 percent to close at 0.77 dirham, off an early high of 0.79. More than 85 percent of the market's traded volume was Dana shares.
On Monday, Dana had jumped 14.1 percent on news that the government of Iraqi Kurdistan had agreed to immediately pay Dana's gas production consortium $1 billion, including $400 million for investment in the region.
Dana is due 35 percent of the money, which it said on Tuesday the consortium had already received.
In addition to payment, the deal is expected to permit the consortium to boost output sharply. Majid Jafar, managing director of the board of Dana, told Reuters that the consortium would raise production within two years from the current 330 million cubic feet a day to 800 million - enough to supply the annual gas needs of a country the size of Austria.
"This is only the next phase. These fields could potentially produce several times more," he said.
Dubai's index fell 0.3 percent but amusement park operator DXB Entertainments, the most active stock, added 0.6 percent, rebounding for a third straight day from a month-long downtrend.
Egypt's index was flat as the market reopened after Eid. The most heavily traded stock, investment firm Qalaa Holdings, climbed 3.2 percent.
Global Telecom, however, pulled back 4.1 percent. Last Wednesday, its previous trading day, it had jumped 7.6 percent after the company and its parent Veon said their subsidiary in Pakistan, Jazz, had signed an agreement for the sale of its tower business for approximately $940 million.
Markets in Saudi Arabia and Qatar remained closed for Eid holidays and will reopen on Wednesday.