Rhetoric continues to drive the oil market as market watchers seek production interventions amid the crude glut.

The latest to join the Middle East's production freeze discussion is Kuwait, which produces 3 million barrels of oil per day. The country said Tuesday that it will freeze output only if all major producers participate, including Iran, which is publicly against a freeze.

After the news, the internationally traded Brent broke a six-day winning streak to settle down 3 percent at $39.65 on the day. In the same vein, WTI settled down nearly 4 percent at $36.50.

While OPEC and other oil producing countries mull over a freeze, Chevron CEO John Watson told CNBC that the company expects U.S. oil production to decline by about 100,000 barrels per month, month over month.

"A million barrels per day of surplus production is starting to dissipate and that's why you're seeing some strengthening in the oil markets over the last couple of weeks," he told "Closing Bell."

"Markets are forward-looking and while oil is being produced in surplus to what demand is today, we're starting to see that change."

The energy giant announced spending cuts and a dividend increase during its annual securities analyst meeting Tuesday. While Watson cited "tough conditions" in the oil industry, he said that Chevron (NYSE: CVX) will continue supporting dividend growth, as it has for the last 28 years.

In addition, the company announced on Monday that it started producing liquefied natural gas and condensate at its Gorgon Project on Barrow Island off Australia.

Chevron's natural gas endeavor concerns market watchers given that domestic natural gas prices have been declining, but the EIA reports that lower prices have propelled natural gas exports. Watson said its consumers will be the Japanese and Korean market, two of the largest LNG consumers, according to the EIA.

"Prices are under pressure both oil and gas; natural gas prices in this country are very low, and LNG prices that are on a spot market are low. But we've sold 75 percent of our gas on our two big projects in Australia to oil linked pricing going forward," Watson said.

"As we start to see some strengthening in the oil markets we think that we will be growing production into a rising market," he added, noting that Chevron foresees its Gorgon Project will be profitable in a $40 oil environment.

— Reuters contributed to this report.

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