* Qatar National Bank pulls down Qatari index
* Gulf Warehousing rebounds near pre-sanctions level
* Emaar Properties supports Dubai market on spin-off plan
* Dana proposes to restructure $700 mln sukuk at lower rates
* Trade very thin in Saudi Arabia
By Andrew Torchia
DUBAI, June 13 (Reuters) - Gulf stock markets were mixed on Tuesday as Qatar fell back, still affected by other Gulf states' sanctions against Doha, while Abu Dhabi's Dana Gas soared on its proposal to restructure a $700 million sukuk.
Qatar's index fell by 0.4 percent but remained more stable than when the sanctions were announced last week.
Qatar National Bank, the region's largest lender, fell by 1.3 percent. Like other Qatari banks, it has been hit by concern that the economic and diplomatic boycott imposed by Saudi Arabia and its allies could reduce its access to foreign funding. However, some other lenders held firm, with Doha Bank up 0.2 percent.
Logistics company Gulf Warehousing, which had plunged after the boycott started, rebounded 6.9 percent to 48.80 riyals.
Though Qatar's trade has been disrupted, it has kept shipments moving thanks to measures such as changing shipping routes to operate via Oman instead of the United Arab Emirates.
Dubai's index rose 0.4 percent as Emaar Properties rose 1 percent, building on gains after last week's announcement of plans to spin off its local real estate business.
In Abu Dhabi, the index climbed 0.6 percent as Dana Gas jumped by its 15 percent daily limit to 0.69 dirhams, its highest level since late 2014. Trade in the stock was at its heaviest for three years.
The company said it was proposing to restructure its $700 million of outstanding sukuk at much lower profit rates because it had discovered the paper was "unlawful" in the United Arab Emirates -- a claim that some creditors said they would contest.
Saudi Arabia's index was almost flat in thin trade but Gulf Union Cooperative Insurance jumped by its 10 percent daily limit after saying it had cut its accumulated losses to 20 percent of capital from 33.5 percent.
* The index edged down 0.03 percent to 6,821 points.
* The index gained 0.4 percent to 3,442 points.
* The index added 0.6 percent to 4,538 points.
* The index fell 0.4 percent to 9,095 points.
* The index rose 0.3 percent to 13,531 points.
* The index edged up 0.03 percent to 6,777 points.
* The index rose 0.4 percent to 1,327 points.
* The index was flat at 5,314 points. (Editing by David Goodman)