* Ukrainian drone targets Russian naval base at Novorossiysk

* Attack near grain hub heightens war risks to Black Sea trade

* Wheat rallies further after India says may scrap import tax

* Corn, soybeans also higher

CHICAGO, Aug 4 (Reuters) - Chicago wheat climbed on Friday after a Ukrainian drone attack near a Russian Black Sea export hub, rekindling global supply fears while India raised demand expectations as it considers scrapping wheat tariffs.

Soybeans climbed on stronger crude and vegetable oil markets, also on alert following the Black Sea disruptions.

Corn followed wheat higher.

Chicago Board of Trade most active wheat added 5 cents to $6.32 a bushel, after climbing to $6.53-3/4 overnight. Wheat futures are poised for a nearly 10% weekly decline.

CBOT corn gained 3-1/4 cents to $4.96-1/2 a bushel, but could end the week 6% lower.

Soybeans firmed 10-1/2 cents to $13.35-3/4 a bushel. For the week, soybean futures are likely to be down more than 3%.

Ukrainian sea drones attacked a Russian navy base near the port of Novorossiysk, a major terminal for Russian grain and oil exports. The port temporarily halted all ship movement before resuming normal operations.

"There was some destruction, but the port is still working," said Tom Fritz, commodity broker at EFG Group. "Markets get emotional, we get these middle of the night spikes, but as long as these ports continue to work, what's the point of sustaining the rally?"

Disruption of Russian shipments through the Black Sea, in addition to already curtailed Ukrainian exports, could unsettle the wheat market, traders said, but like after recent Russian strikes against Ukrainian grain ports, participants were assessing the actual impact on export markets.

Wheat was further boosted by the possibility that India is considering cutting or abolishing import taxes on wheat.

India's food secretary rejected reports of a deal to import Russian wheat, though the country could increase imports to cool domestic prices.

"There's a disparity between India's wheat production, officially, and what some of the larger private firms and some of the vegetation density maps and satellite imagery would suggest. And this compounds the problem of their rice crop as well," said Mike Zuzolo, president of Global Commodity Analytics.

Strength in corn and soybeans due to global supply uncertainty was capped by weather forecasts for improving weather for U.S. crops and uncertain demand. (Reporting by Christopher Walljasper; additional reporting by Gus Trompiz in Paris, Naveen Thukral in Singapore and Michael Hogan in Hamburg; editing by David Evans)