* Euro at six-week low vs dollar in broad market sell-off
* Italian official in anti-euro comments, then rows back
* Dollar rallies across the board
* Yen, Swiss franc gain as markets slide
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh (Adds graphic, updates prices)
By Tommy Wilkes
LONDON, Oct 2 (Reuters) - The euro fell to a six-week low on Tuesday after a senior lawmaker in one of Italy's ruling parties said most of the country's problems would be resolved if it readopted a national currency, triggering a broad market sell-off.
The euro also slumped against the safe-haven yen and Swiss franc, while the dollar surged to a one-month high as investors piled in and sold riskier assets such as equities.
Markets are highly sensitive to Italian political developments after the country's coalition proposed a budget with a higher-than-expected deficit target, exacerbating tensions with other euro zone leaders and worrying investors who want Rome to bring its debt under control.
The lawmaker, Claudio Borghi, later rowed back on the comments, while Prime Minister Giuseppe Conte said the euro was "unrenounceable". .
But that failed to ease pressure on the single currency , which skidded as low as $1.1505, its weakest since Aug. 21. Against the yen, the euro lost almost one percent to 130.71 before recovering some ground, and dropped 0.6 percent versus the Swiss franc to 1.1313 francs.
"We are dealing with a war of words, with the euro on one side and Italy on the other ... There's a lot of headline risk about," Credit Agricole head of G10 FX Strategy Valentin Marinov said.
Marinov did not expect the situation in Italy to weigh heavily on the euro in the medium term because there was "no real evidence of contagion" that would worry the European Central Bank and prompt it to postpone plans to end its stimulus programme.
The euro's weakness combined with a further push higher by the dollar, which is regaining its stride despite investor positioning in the greenback looking stretched.
Most of the common currency's losses came after Borghi, the economic head of the right-wing League party, said Italy would enjoy more favourable economic conditions outside the euro zone.
Deputy Prime Minister Luigi Di Maio, who accuses European Union officials of deliberately upsetting financial markets with negative comments about Italy's budget plans, also unnerved investors by reiterating that it would not change its fiscal deficit targets.
Even if the EU does not reject Italy's budget, it could still act as a hurdle for the euro, Commerzbank FX strategists said, especially as some analysts expect credit ratings agencies shortly to downgrade Italy's government debt.
"Even if the subject (of Italy) seems to remain on the back burner for the FX market at present, market participants should keep a close eye on it. It can cook up more rapidly than we think," they wrote.
The dollar index rose 0.4 percent to 95.693, a six-week high.
Fears about a rumbling U.S./China trade conflict have lifted the dollar this year, as has an increasingly confident U.S. Federal Reserve, which looks to be more and more alone in tightening policy.
Against the yen, the dollar fell 0.2 percent to 113.78 yen on the Japanese currency's safe-haven status.
A U.S.-Canada trade deal announced on Monday had sent the yen to an 11-month low of 114.06 per dollar as the agreement boosted investor appetite for risk.
The Australian dollar - often viewed as a barometer of risk appetite - fell 0.9 percent $0.7162 as markets worldwide were spooked by the euro zone concerns. The Reserve Bank of Australia earlier held interest rates at 1.5 percent, a widely expected decision.
The Canadian fell 0.2 percent to C$1.2840 per dollar, reversing some of its gains on Monday.
Sterling, hit both by the broader market tumble and the latest Brexit nerves, skidded 0.7 percent to as low as $1.2941.
editing by John Stonestreet