* Trade dispute between U.S. and China has rattled markets
* U.S., China are world's two biggest oil consumers
* China promise to open economy further, lower import tariffs
* Oil prices generally supported by OPEC-led supply restraint
* Soaring U.S. output undermines OPEC efforts to prop up prices
* China seeks alternative to Saudi supplies (Adds Xi Jinping statement on trade, updates prices)
SINGAPORE, April 10 (Reuters) - Oil markets rose for a second day on Tuesday on hopes that a trade dispute between the United States and China, the world's two biggest crude consumers, may be resolved without greater damage to the global economy.
Yet prices remain within recent ranges as oil markets still face an abundance of supply that puts pressure on producers to keep their prices competitive in order not to lose market share.
Brent crude futures were at $68.97 per barrel at 0417 GMT, up 32 cents, or 0.5 percent, from their last close.
U.S. West Texas Intermediate crude futures were at $63.76 a barrel, up 34 cents, or 0.5 percent.
The gains followed a more than 2 percent rally on Monday during European and American trade hours, but that was a rebound from a 2 percent decline on Friday.
Chinese President Xi Jinping on Tuesday promised to open the country's economy further and lower import tariffs, in a speech that struck a conciliatory tone on the rising trade tensions between China and the United States.
Concerns of a prolonged trade dispute between the world's two biggest economies and uncertainty over the supply and demand balance of global oil markets have resulted in volatile recent trading. A trade dispute between the U.S. and China could lead to slower economic growth that would limit oil demand.
Beyond the trade dispute, oil markets are also concerned about the potential of renewed U.S. sanctions against some significant oil producers.
"In addition to the risk of protectionism, there has been a significant change in the Trump administration that has raised risks of potential sanctions on key oil exporting countries including Iran, Venezuela and Russia," U.S. bank JPMorgan said.
Traders said weekly U.S. fuel inventory data would provide further market guidance.
The American Petroleum Institute will publish storage data later on Tuesday while official data from the U.S. Energy Information Administration is due on Wednesday.
U.S. crude inventories are expected to gain slightly from the previous week as refinery runs edge lower and product stockpiles are forecast to decline, according to a Reuters poll on Monday.
Oil markets have been supported by healthy demand and supply cuts led by the Organization of the Petroleum Exporting Countries (OPEC).
However, soaring U.S. crude production <C-OUT-T-EIA>, which has jumped by a quarter since mid-2016 to 10.46 million barrels per day (bpd), is threatening to undermine OPEC's efforts to tighten the market and prop up prices.
The U.S. late last year overtook Saudi Arabia as the world's second-biggest crude producer. Only Russia pumps more crude, at almost 11 million bpd.
In a sign that oil supplies remain ample, China's Sinopec , Asia's largest refiner, plans to cut Saudi crude imports in May by 40 percent, instead buying from alternative sources, after Saudi Aramco set higher-than-expected official prices, a company official said on Monday.
JPMorgan said it expects Brent and WTI prices to average $69.50 and $65.20 per barrel in 2018, respectively, while it forecasts $64 per barrel for Brent and $58.50 per barrel for WTI in 2019.
(Reporting by Henning Gloystein; Editing by Richard Pullin and Christian Schmollinger)