* ECB's Lagarde says negative rates to end soon
* Dollar drops across the board, follows sell-off last week
* Aussie adds 1%, but election reaction limited (Adds Lagarde comments, new quote, latest prices, chart)
LONDON, May 23 (Reuters) - The euro rallied on Monday after the European Central Bank president said policymakers would likely lift interest rates out of negative territory by September, while the dollar extended its recent slide.
A calmer mood on equity markets in European trading also pressured the dollar, which fell sharply last week but has been the go-to currency for investors this year when risk assets tumbled and worries about the economy and inflation jumped.
The euro was the big gainer, adding as much as 1.1% to $1.0687. It has now risen 3.3% since hitting a multi-year low of $1.0349 on May 13.
ECB President Christine Lagarde said in a blog post that the bank was likely to lift the euro area deposit rate out of negative territory by end-September and could raise it further if it saw inflation stabilising at 2%.
The euro's rally came as the dollar fell broadly, with a sell-off that began accelerating last week.
"We see this as just a temporary correction (in the U.S. dollar) for now. If we look at the main reasons why the dollar has been strengthening so much in recent months, we don't think that fundamental story has changed significantly over the past week," said MUFG analyst Lee Hardman.
"But in the very short term there is a risk that this correction lower could extend further," he added, pointing to a build-up in long dollar positions in recent weeks that leaves the market vulnerable.
The U.S. dollar index, up about 16% to a two-decade high to 105.01 over the 12 months to the middle of May, fell 0.8% on Monday to 102.15.
The Australian dollar, which initially showed a muted reaction to the victory for the centre-left Labor Party in national elections at the weekend, climbed 1% to $0.7125 .
The Japanese yen rose to 127.47 yen per dollar.
The euro also rose 0.3% versus the Swiss franc to 1.0315 francs, undoing some of the franc's gains since the Swiss National Bank chairman last week said policymakers were ready to act if inflation strengthened.
Sentiment around China also helped riskier currencies. Shanghai is edging out of lockdown, and an unexpectedly big rate cut in China last week reassured investors.
The yuan had its best week since late 2020 last week and in offshore markets on Monday firmed to 6.6542 per dollar , its strongest since early May.
Geopolitics are also in focus in Asia this week as U.S. President Joe Biden tours the region.
Commodity-linked currencies climbed, with the Norwegian crown up 0.5% versus the euro and the Canadian dollar rising by a similar amount.
The U.S. dollar has soared this year but with expectations for repeated Federal Reserve interest rate hikes priced in, some analysts say further gains may be tougher from here.
Others say the macroeconomic backdrop still points to more downside for the euro, however.
"The Ukraine war keeps fuelling geopolitical uncertainties and recession risks mostly in Europe," said Thomas Hempell, head of macro & market research at Generali Investments.
"As inflation soars globally and lockdowns choke off growth in China, policy uncertainty keeps benefitting the anticyclical USD."
(Reporting by Tommy Wilkes; Additional reporting by Tom Westbrook in Singapore; Editing by Jan Harvey)