(Adds more comment, updates prices)
* Euro little deterred by note of caution from ECB sources
* Canadian dollar nears C$1.30, sterling $1.30
* Dollar gains a third of a percent against the yen
* Graphic: World FX rates in 2017 tmsnrt.rs/2egbfVh
By Patrick Graham
LONDON, June 29 (Reuters) - The euro jetted past $1.14 to its highest in just under 14 months on Thursday, with attempts by European Central Bank sources to moderate the message taken from a speech by President Mario Draghi this week falling largely on deaf ears.
Three days of the biggest gains in more than a year for the single currency have pushed the broader dollar index to its lowest since October and prompted some of the market's biggest dollar supporters to call the currency's rally over.
Draghi's speech on Tuesday - coming amid a raft of hawkish signals from other major global central banks - convinced markets the ECB was preparing to start withdrawing its own emergency stimulus for the euro zone economy later this year.
After a long run lower, that has put the euro back in relatively uncharted territory, some analysts argue there is little technical resistance beneath $1.20. The currency steadied around $1.14 as U.S. traders arrived at their desks on Thursday.
"The biggest test will be 1.1500," said RBC's head of global FX strategy Elsa Lignos.
"Though month-end USD selling may reinforce the bearish USD sentiment in the next few days, we still think EUR’s rally is more likely to run out of steam at 1.15."
The euro was also half a percent higher against the yen at 128.435 yen. A third of a percent gain for the dollar against the yen also pointed to a slightly more robust performance for the dollar as the European morning wore on.
"The July 4 holiday is on Tuesday, so a lot of the U.S. community will take the Monday off," said Richard Benson, co-head of portfolio investment with currency fund Millennium Global in London. "That means we are entering the quarter-end already today."
"It may be a bit illiquid and a bit messier from here."
The other big gainers among the G10 group of major developed world currencies over the past 24 hours were the Canadian dollar and sterling, both also driven by comments by their respective central bank governors.
Sterling gained another third of a percent in morning trade in London, briefly topping $1.30 for the first time in five weeks.
Eyes were also shifting to other central banks, including Sweden's Riksbank, which meets next week and has previously resisted tightening monetary controls in an economy that has generally been growing strongly for two years.
"This is simply the central banks getting together and trying to arrest inflation," said Nomura's head of G10 currency trading Peter Gorra of the messages sent by officials in the past week.
"They are trying to be as smart as they can and agreeing that they have to act in unison. I don't think this is necessarily a dollar move and I don't think the dollar's rally is over. They are just trying to add some two-way risk to the market."
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Editing by Jon Boyle)