* Euro trades within range vs dollar * Single currency expected to hold above $1.28 * Australian, Canadian dollars fall to 4-week lows By Jessica Mortimer LONDON, Oct 3 (Reuters) - The euro steadied against the dollar on Wednesday, underpinned by the belief that Spain will eventually request financial aid, a move which would prompt the European Central Bank to buy Spanish bonds and boost the euro. It remains uncertain when Spain will make the move, however, after Prime Minister Mariano Rajoy on Tuesday quashed speculation the country could apply for a bailout as soon as this weekend. The single currency was flat at $1.2924, staying well above the three-week low of $1.28035 hit on Monday and with the potential to test Tuesday's peak of $1.2968. "We expect Spain to apply for aid and relatively soon, within the next one to three weeks ... This will be a further relief for the euro but it's still not solving the underlying problems of the euro zone," said Richard Falkenhall, currency strategist at SEB in Stockholm. "It's reasonable to see people cutting back on short euro positions, but it's hard to believe that medium to long-term investors would be setting long euro positions." He said a Spanish bailout request would push the euro above $1.30, perhaps towards $1.35 but not further. A euro zone purchasing managers' survey on services and retail sales data highlighted concerns about the region's very weak economy. The numbers did not dent the euro as they were slightly less bad than some in the market had feared. The euro's movements are likely to be limited before Thursday's European Central Bank meeting and U.S. jobs data on Friday, which could trap the euro in a range between $1.28 and $1.2968, strategists said. "All eyes at the moment are on non-farm payrolls on Friday. If we get a reasonably good number that will be risk on across the board and euro will grind higher. So from a short-term trading perspective the strategy should be buy on dips," said Peter Kinsella, currency strategist at Commerzbank. U.S. private payrolls figures are due at 1215 GMT and may give a hint of how the non-farm numbers will look. Despite continuing weak euro zone data, few market players are expecting the ECB to cut rates from an already record low of 0.75 percent on Thursday. The common currency was also helped by Moody's saying it would announce the results of its review of Spain's sovereign debt rating some time this month, wrongfooting euro bears who had expected an imminent downgrade. Spain stands to lose its investment grade rating if Moody's decides on a downgrade. GROWTH-LINKED CURRENCIES STRUGGLE The Australian dollar fell broadly and other commodity- and growth-linked currencies like the Canadian dollar followed suit after Australia posted its biggest trade deficit in 3-1/2 years as falling prices for iron ore and coal dented export earnings. The euro rose to a 3-1/2 month high of A$1.2664, while the Australian dollar also fell against the U.S. currency to US$1.0198, its lowest level since Sept. 6. Against the Canadian dollar, the U.S. dollar also hit a near four-week high of C$0.9878. The Aussie was also weighed down by expectations that domestic interest rates will be cut further, after the Reserve Bank of Australia on Tuesday cut its cash rate by 25 basis points to 3.25 percent, the lowest level in three years. But further falls for the Australian currency could be limited as the U.S. Federal Reserve and European Central Bank are busy trying to stimulate their economies as well, diminishing the allure of both the dollar and euro. Against the yen the dollar rose to a near two-week high of 78.31 yen. Traders said they saw dollar buying by U.S. corporates.