Global benchmark Brent crude prices were down 61 cents at $36.61 a barrel at 1503 GMT (8:33 p.m. in India). US West Texas Intermediate (WTI) crude slipped by 40 cents to $36.36.
"It is the Chinese stock market sell-off and the strong dollar that are pressuring oil," said Tamas Varga, oil analyst at London brokerage PVM Oil Associates.
Chinese stock markets fell again on Tuesday after a 7 per cent dive on Monday, rattling markets worldwide and prompting action from the central bank and stock market regulator.
Concerns about the economy in China, the world's second-largest oil consumer, were worsened by news that national rail freight volumes logged their biggest ever annual decline in 2015.
"Last year we talked about supply and demand even surprised on the upside. But with this news flow from China, demand fears have come back," said Frank Klumpp, oil analyst at Stuttgart-based Landesbank Baden-Wuerttemberg.
The US dollar hit a one-month high against a basket of currencies, weighing on oil prices as it made holding dollar-denominated commodities more expensive.
The oil market largely shrugged off rising political tensions in the Middle East. On Tuesday Kuwait recalled its ambassador to Iran after attacks on Saudi missions by Iranian protesters, state news agency KUNA reported.
Analysts said that as long as the conflict did not affect oil production in the region it would not have a consequence for oil prices.
ANZ bank said the tensions between Saudi Arabia and Iran will "reduce the likelihood of any collaboration between the two oil majors regarding oil output as Iran re-enters the international market once sanctions are lifted".
A Reuters survey found that OPEC (Organization of Petroleum Exporting Countries) oil output fell in December, led by lower supply from Iraq after a record-breaking November. Exports from Iraq's southern terminals, its main outlets, fell in December but are likely to reach new highs again in the coming months.
In Libya, Islamic State militants resumed attacks on oil infrastructure, hitting a storage tank in the port of Es Sider.
This followed clashes on Monday, during which a storage tank holding about 400,000 barrels of crude exploded.
The ports are not operating, but analysts said that Islamic State's growing presence in oil-rich Libya means the country is unlikely to regain pre-crisis production levels any time soon.
In Algeria, an explosion and fire at the Skikda oil refinery injured 18 people, but production was unaffected because the incident occurred in a unit used to fill butane bottles.
Data from US industry group American Petroleum Institute, expected at 2130 GMT (3:00 a.m. in India), will give an indication of US crude inventory levels.
Genscape data published on Monday showed crude inventories at Cushing, Oklahoma, had reached a record high in the week to January 1, though a Reuters poll indicated that stocks had fallen by 500,000 barrels.
© Thomson Reuters 2016