SYDNEY, July 13 (Reuters) - The Australian and New Zealand currencies fell on Monday as intensifying fighting in the Gulf pushed oil prices higher, reviving inflation fears and driving investors into the safety of the U.S. dollar.

U.S. and Iranian forces exchanged heavy missile and drone assaults on the weekend, with Tehran targeting U.S. facilities in states across the Gulf on Sunday and saying it had again closed the vital Strait of Hormuz.

The risk-sensitive Aussie AUD=D3 lost 0.3% to $0.6931, erasing last week's small gain of 0.2%. Near-term resistance is at $0.6980 while support is at the 14-day moving average of $0.6921.

The kiwi dollar NZD=D3 slipped 0.2% to $0.5749. That followed a rally of 1% last week as its central bank raised interest rates for the first time in over three years and markets wagered on more. Resistance is at a three-week high of $0.5791.

Those declines came in tandem with a jump of 4.3% for Brent crude futures to $79.23 a barrel on Monday O/R and a retreat in stocks during Asian time.

It is a thin week for Australia's economic calendar.

But the kiwi could find support from a speech by the Reserve Bank of New Zealand's chief economist Paul Conway on Tuesday where he is expected to talk about the implications of oil shocks and inflation. A quarterly survey of business opinions may also shed some light on firms' pricing behaviours.

"The speech will provide him an opportunity to affirm Governor Breman’s recent hawkish comments or, alternatively, push back against current market pricing," said Joseph Capurso, head of foreign exchange at the Commonwealth Bank of Australia.

Swaps now imply a 75% probability that the RBNZ will deliver a follow-up rate hike in September and are fully pricing in two more rate hikes this year.

Those reasons helped New Zealand's 10-year bond yields NZ10YT=RR rise 2 basis points on Monday to 4.635%, on top of a 14-bp climb last week to their highest since late May.

That in turn helped flip the spread with Treasuries back to a positive 5 bps, having been as low as negative 7 bps in recent days, providing support to the kiwi.

In contrast, investors suspect the Reserve Bank of Australia could be done hiking after three rate rises to 4.35%, with a further move this year just seen at around 50%. The Aussie lost 0.3% to NZ$1.2026 AUDNZD=R to hover near a six-week low.