(Adds budget detail) SYDNEY, May 11 (Reuters) - The Australian and New Zealand dollars held near 10-week highs on Tuesday as strength in global commodity prices helped offset a slide in share markets, while Australia’s government handed down a big spending budget to fuel growth. The Aussie hovered at $0.7843, after touching a top of $0.7891 overnight. The next major bull target is the February peak just above $0.8000, while support comes in around $0.7825 and $0.7790. The kiwi dollar stood at $0.7284, having also reached a 10-week top at $0.7304. Its February peak is all the way up at $0.7463, while support lies at $0.7260 and $0.7245. Both were underpinned by strength in commodities, with the Aussie energised by a remarkable 10% surge in iron ore prices to record highs. The steelmaking mineral is Australia’s single biggest export earner, worth A$150 billion in the year to March. “The “melt up” in commodity prices over the last week has added significant weight to that view that the A$ remains undervalued,” said Richard Franulovich, head of FX strategy at Westpac. “We used the dip below $0.7680 earlier last week as an opportunity to trigger our buy recommendation. Dips should now be limited into the $0.7785 and $0.7820 region.” The jump in iron ore to over $200 a tonne has been a huge tax windfall for the Australian government, which had budgeted for prices of just $55 a tonne. That was one reason it managed a budget deficit of A$161 billion, down from the previous projection of A$197.7 billion, though it was still by far the largest on record. It was also higher than some analysts had predicted, as was the projected deficit for 2021/22 of A$107 billion. That means the government needs to sell less debt than first feared, which should support the country’s triple A credit rating and bond prices. Reserve Bank of Australia (RBA) Deputy Governor Guy Debelle recently noted the central bank was now often buying more bonds in a week than the government was selling. That has helped keep 10-year yields down at 1.68%, near their lowest since early March and a slim 7 basis points above U.S. yields. ($1 = 1.2781 Australian dollars) (Editing by Jacqueline Wong and Subhranshu Sahu) Our Standards: The Thomson Reuters Trust Principles.