Aug 8 (Reuters) - The Russian rouble weakened past 96 against the dollar on Tuesday, heading back towards a more than 16-month low hit in the previous session, hampered by strong local demand for foreign currency.

The rouble had recovered on Monday to post daily gains for the first time in August, but gave those up early on Tuesday. The rouble last week dropped more than 4% against the dollar and euro to record one of its worst weeks all year.

At 0718 GMT, the rouble was 0.8% weaker against the dollar at 96.08, sliding back towards 97.0625, its weakest point since March 25, 2022, hit in the previous session.

It lost 0.4% to trade at 105.71 versus the euro . It shed 0.4% against the yuan to 13.30 .

The rouble tends to weaken early each month after losing support of a month-end tax period that usually sees exporting firms convert foreign exchange (FX) revenue to meet local liabilities.

Market players have also attributed the rouble's jitters to Western companies' exits from Russia, which can require large FX purchases and foster currency market volatility.

Russian authorities say lower export revenue and rebounding imports are the primary cause of rouble weakening.

Brent crude oil, a global benchmark for Russia's main export, was down 0.8% at $84.70 a barrel, but still close to Monday's near four-month high.

Russian stock indexes were lower.

The dollar-denominated RTS index was down 1.5% at 1,002.1 points. The rouble-based MOEX Russian index was 1.1% lower at 3,050.8 points.

Continued rouble weakness and bullish expectations on oil prices are supporting the MOEX index, which on Friday hit its strongest point since before Russia's February 2022 invasion of Ukraine, said Sinara Investment Bank.

"Even an overheated market should not be underestimated, and this week we could again see a run to 3,200 points if the rouble continues to weaken," Sinara said in a note.

For Russian equities guide see

For Russian treasury bonds see

(Reporting by Alexander Marrow; Editing by Susan Fenton)