Italian borrowing costs hit euro lifetime peaks at a debt auction on Tuesday as investors demand ever higher premiums to keep funding the country, in a sign that the sovereign debt crisis is nearing make-or-break point.

The yield on a new three-year Italian government bond soared to almost 8 percent, a level seen driving its financing costs to unaffordable levels if sustained for a long time.

The new three-year paper was trading at yields around 8 percent in the gray market before the auction, over 40 basis points more than the July 2014 bond, according to prices on Reuters.

Analysts said the huge rise in the yield on the three-year maturity -- last sold at the end of October at 4.93 percent -- supported demand and helped the Treasury place the target range of 2.5 billion to 3.5 billion euros planned for the first tranche.

In total, it sold 7.5 billion euros of bonds, close to the upper end of its target range.

These are good auctions in terms of the amount of bids, size issued ... but the ever higher yields remain the concern, said Peter Chatwell, interest rate strategist at Credit Agricole.

In an ideal world these yields, and the fact that the three-year was above 8 percent in the gray market this morning, would serve to give the EcoFin/Eurogroup a sense of added urgency, but this is a far from ideal world.

The Italian auction is the latest in a barrage of closely watched euro zone debt auctions as the crisis spreads beyond the bloc's weaker economies. An estimated 19 billion euros worth of debt is being auctioned this week, with Spain and France due to tap the market on Thursday.

The yield for the 10-year bonds was 7.56 percent, compared with 6.06 percent at a previous sale a month ago. Ten-year yields traded around 7.6 percent in the secondary market.

Italian government bond yields and German Bund futures fell, while European stocks and the euro rose after the auctions in a move strategists said was relief that the country managed to sell debt in volumes close to the upper end of its target range.

But concerns remain about the continuing rise in costs.

On Friday, Italy paid a euro lifetime high yield of 6.5 percent to sell new six-month paper at a poorly received auction, which sent two-year yields spiraling above 8 percent.

Pressure eased somewhat on Monday after a weekend report in Italian daily La Stampa that the International Monetary Fund was preparing a rescue plan worth up to 600 billion euros for Rome. An IMF spokesman denied the report.