Oil prices fell back in choppy trading on Tuesday after earlier gains, as fading hopes for a US-Iran deal to reopen the Strait of Hormuz continued to weigh on markets. Brent North Sea Crude was down 0.7 percent at $87.12 per barrel and West Texas Intermediate down 0.6 percent at $8.64 per barrel, after both had risen more than two percent earlier in the session. Stock markets were marginally higher, with the Dow up 0.3 percent and the S&P 500 up 0.1 percent, while the tech-heavy Nasdaq opened lower. Analysts noted that reduced expectations for Federal Reserve rate hikes following a weak US payroll report supported equities, but rising crude prices and the Hormuz impasse introduced fresh inflation risks. Attention now turns to US consumer price data on Wednesday, which could guide the Fed's next move.