LONDON, June 1 (Reuters) - The U.S. dollar was steady on Monday after a small weekly loss as investors awaited developments in Middle East peace talks and U.S. jobs data later this week that could shape the Federal Reserve's monetary policy path.

The dollar index, which measures the currency against six peers, edged lower last week on expectations that a deal between the United States and Iran to reopen the Strait of Hormuz was close. The closure of the key oil artery has lifted oil prices and worsened the inflation outlook, leading some to expect the Fed to raise rates this year.

But with little fresh insight into the progress of peace talks and a flare up of hostilities between the U.S. and Iran over the weekend, currency markets are in wait-and-see mode. 

"We're waiting to see some progress in one direction or another," said Tommy von Brömsen, FX strategist at Handelsbanken. 

Should the Strait of Hormuz reopen to traffic and oil prices come down, the dollar would likely weaken in the near term and risk-sensitive currencies, such as the Swedish crown, would outperform, von Brömsen added. 

The dollar had rallied at the onset of the conflict, buoyed by safe-haven demand and the U.S. economy's relatively limited exposure to energy-driven inflation. However, it has given back some of those gains due to uncertainty surrounding the conflict's trajectory.

The dollar index was little changed on the day at 99.02 after last week's drop of 0.4%.

The euro was down slightly at $1.1652, while sterling edged up 0.1% to $1.3460.

FED WATCH 

Markets are betting the Fed's next move will be to raise its key rate, compared with expectations for a cut before the start of the Iran war, given rising energy prices and the impact they will have on inflation, and a still-resilient jobs market. 

The U.S. labour market figures due on June 5 could help sway what the Fed will do in the near term. The data are expected to show a steady unemployment rate of 4.3% and an increase of 85,000 jobs, according to a Reuters poll of economists. 

Fed Governor Jerome Powell, whose term as chair formally ended on May 15, warned in a speech on Sunday about politicisation of monetary policy. Powell has decided to continue as a Fed governor in part because of what he regards as ongoing threats to the Fed's independence. 

The Fed's Beth Hammack, Lorie ​Logan, and Mary Daly are among policymakers due to speak later in the week.

YEN IN FOCUS

A speech by Bank of Japan Governor Kazuo Ueda on Wednesday is highly anticipated for signals as to whether the central bank will proceed with a rate increase the following week.

While there is no consensus yet within the BOJ on the decision, a pause in the central bank's taper of government bond purchases is increasingly seen as a preferred option, said two sources familiar with the deliberations.

The yen weakened 0.1% to 159.45 per dollar, close to the psychologically important 160 level that saw intervention by Japanese authorities to strengthen the currency.

"It seems like 160 is where they draw the line," said Handelsbanken's Tommy von Brömsen. 

"I think there will be intervention if we approach that level again."

The Australian dollar traded flat at $0.7179 against the dollar, while New Zealand's kiwi slid 0.4% to $0.5969.