Australia central bank warns rate hikes might not be over after holding fire

* RBA holds rates, but cautions it may not be done with hikes

* RBA says inflation is still too high, notes Gulf deal is welcome

* Markets muted as decision widely expected; A$ down a tad

* Swap markets imply small chance of rate hike in Aug (Adds comments from Governor Michele Bullock at press conference)

By Stella Qiu and Wayne Cole

SYDNEY, June 16 (Reuters) - Australia's central bank held its cash rate steady at 4.35% on Tuesday, saying the economy was slowing in the face of tighter financial conditions but warned it might yet hike again if needed to control inflation.

Wrapping up its June policy meeting after pausing for the first time this year, the Reserve Bank of Australia (RBA) said inflation was still too high and it would do whatever necessary to bring it down, "including increasing the cash rate target further if required."

Markets had wagered on a steady outcome following a run of softer domestic data on inflation, consumer demand and employment, while a peace deal in the Middle East to reopen the Strait of Hormuz had pulled down oil prices and lessened inflation risks.

Governor Michele Bullock said the board did not consider a rate hike this time but remains concerned about inflation and wouldn't rule out another increase.

"Reports that an agreement has been reached to end the conflict in the Middle East are welcome," Bullock said at the post-meeting press conference.

"If the conflict does end and the Strait of Hormuz is reopened, this should support the flow of commodities and lower prices, but this could take some time and an orderly resolution is still not assured, meaning there are still upside risks to inflation and downside risks to growth."

The unanimous decision was largely as expected. The Australian dollar held onto earlier losses and was down 0.3% at $0.7050. Swaps imply around a 26% chance of a move in August, and just a total tightening of 13 basis points for the year, equivalent to less than one rate hike.

"With inflation taking precedence over growth for the time being, it is too soon to expect any dovish shift in the Bank's broader narrative about monetary policy," said Sally Auld, chief economist at National Australia Bank.

"Accordingly, we think it appropriate that the market retains some chance of tightening in the next few months."

ECONOMIC SLOWDOWN AS EXPECTED

The RBA has already raised rates by 75 basis points since February as it struggled to contain stubborn inflationary pressures in the face of surging energy costs. Annual inflation slowed to 4.2% in April but a measure of underlying inflation picked up to 3.4%, above the target band of 2% to 3%.

With interest rates now matching their post-pandemic highs, the economy slowed to a crawl in the first quarter, growing just 0.3% at a quarterly pace as consumers tightened their purse strings. The unemployment rate also hit a 4-1/2-year high of 4.5%.

A record run in house prices has ground to a halt, with the government's proposed tax changes driving a sharp drop in demand for new investor loans.

Bullock said the slowdown was as expected and the labour market was still a bit tight.

"I would say you've got to expect a slowing in the economy and when we see it, people shouldn't be alarmed about that. That's what actually has to happen in order to bring inflation down," the governor said.

The RBA charted a softer course than its global peers during the post-pandemic inflation surge, prioritising hard-won gains in the labour market over rapid tightening. Interest rates peaked at 4.35% early last year before three cuts pulled them back to 3.6%, but that strategy backfired as inflation reared its head again.

"The RBA has done enough for now. August is about watching, not moving," said Kellie Wood, head of fixed income at Schroders.

She said if household spending slows on its own, inflation could ease without another rate hike, but warned the pullback could overshoot and trigger a sharper consumption slowdown.

(Reporting by Stella Qiu and Wayne Cole; Editing by Shri Navaratnam)