SINGAPORE, Aug 27 (Reuters) - Shipping traffic at the Strait of Hormuz rose slightly even as a standoff persisted between the United States and Iran, data showed on Thursday, while the market monitored Iran-Oman talks about the waterway.

Visible commodity vessel transits at Hormuz totalled 10 on Wednesday, up slightly from eight on Tuesday, data from Kpler showed. This was below a 10-day moving average of about 15 vessels.

Two medium-range fuel tankers, a liquefied petroleum gas carrier, a Panamax-sized tanker, and three handymax-sized tankers entered the strait from the Gulf of Oman.

A medium-range fuel tanker, a bitumen tanker and a bulk carrier exited the waterway from the Gulf.

Iran and Oman are still working on the details of an agreement on the Strait of Hormuz, a senior Iranian source said on Wednesday, after Iran's Revolutionary Guards said the two countries had agreed how to share the waterway and its revenue.

A tanker was hit by an unknown projectile in the Strait of Hormuz, causing a fire that was later extinguished, the United Kingdom Maritime Trade Operations agency said early on Thursday.

Meanwhile, traffic slowed for a second day at the other key waterway of the Bab el-Mandeb strait.

A total of 19 commodity vessels passed through Bab el-Mandeb on Wednesday, with six tankers that exited, including a very large crude carrier, down from 24 on the previous day, the Kpler data showed.

Some vessels may be sailing at the key waterways with their transponders turned off and may be missed in the counts.

(Reporting by Jeslyn Lerh; Editing by Jacqueline Wong, Christian Schmollinger and Conor Humphries)