(REUTERS) -- The euro fell from six-week highs against the dollar on Monday as a rally driven by short-covering ran out of steam, with investors waiting for a debt swap deal between Greece and its private creditors as well as a summit of EU leaders.

Athens is unlikely to reach an agreement to restructure private sector holdings of its debt in time for the summit, at which Eurozone leaders are expected to sign off on a permanent rescue fund for the Eurozone and agree on inserting a balanced budget rule into national legislation.

Suggestions Greece should give up control of its budget policy to European institutions drew an angry reaction from Greek Finance Minister Evangelos Venizelos, which traders said had also weighed on sentiment.

The single currency fell 0.8 percent on the day to $1.3113 having hit a six-week high of $1.3233 in early trade. It had rallied almost 3 percent last week as speculators covered short positions.

Traders said demand lay near the euro's 55-day moving average at $1.3111.

It looks like we will get a deal on Greece later in the week, but it now looks to be contingent on who will provide the gap in Greece's finances, said Gavin Friend, currency strategist at National Australia Bank.

I think the pullback in the euro today is because maybe the market was expecting something on Greece today and a little bit of optimism has faded, he said, adding he was not expecting the EU summit to have a major market impact.

The Greek debt deal, which would cut the long-term value of privately held bonds by just over 70 percent, is thought to be close, raising hopes that the country at the heart of the Eurozone debt crisis can avoid a messy default.

The talks had run into trouble over the coupon rate and whether the ECB and other public creditors must also take losses on their holdings.

Reflecting negative sentiment towards the euro, data last Friday showed currency speculators boosted their net euro short positions to a record high for the fifth consecutive week in the week ended January 24.

Technical analysts highlighted resistance around $1.3244, the 38.2 percent retracement of the euro's October to January decline.

There's still a huge amount of uncertainty over Greece and that's weighing on the euro. Even if the debt swap is agreed, we still won't know exactly how much they need to borrow said Adrian Schmidt, currency strategist at Lloyds banking Group.

Having said that, the market is massively short euros and there is potential for a sharp move higher if we do get some surprisingly positive news, he added.

The euro inched to a four-month low versus the Swiss franc of 1.2050 francs on trading platform EBS, but traders said large bids around the low were preventing a move towards the SNB's franc cap of 1.2000.

The euro fetched 100.70 yen, down around 0.7 percent on the day but well above a recent 11-year low of 97.04.

Widening Italian and Spanish government bond yields were also hitting the euro, traders said, although an auction of Italian five and 10-year debt had little market impact.

The Australian dollar moved further away from three-month peaks hit in the wake of the Fed's pledge to keep interest rates low, after ratings agency Fitch put major Australian banks on a negative ratings watch.

The Aussie was down 1.1 percent on the day at $1.0543 with traders citing selling by leveraged players amid a pullback in risk appetite.

The drop in riskier assets helped the dollar index bounce 0.4 percent to 79.237, compared with a 6-week low of 78.772 set on Friday.

The dollar stood at 76.70 yen, steadying after two sessions of steep declines. The greenback had come under pressure last week after the Fed signaled it would not hike rates until at least late 2014 and kept the door open to additional stimulus.