* Dollar index down less than 0.1% on day

* Aussie and Kiwi rise 0.5-0.6%

* Graphic: World FX rates in 2020 https://tmsnrt.rs/2RBWI5E

LONDON, Sept 25 (Reuters) - The dollar stabilised below its recent two-month highs on Friday and riskier currencies erased some of their weekly losses, while equity markets got a lift from hopes that U.S. fiscal stimulus talks would resume.

The dollar is on track for it best week since early April, driven by risk aversion that made traders quit their dollar shorts as the outlook for the global economic recovery darkened with a second wave of COVID-19 cases in Europe.

It pulled back slightly on Friday, with riskier currencies, which have fallen sharply this week, gaining in early London trading.

Stocks rose after a late tech-driven rally on Wall Street, with sentiment boosted by a key lawmaker saying Democrats in the U.S. House of Representatives are working on a $2.2 trillion coronavirus stimulus package that could be voted on next week.

The New Zealand dollar rose to 0.6584, up 0.6% since New York's close but still down 2.6% on the week.

The Australian dollar rose 0.5% to as much as $0.7086 at 0724 GMT, but was still having its worst week against the dollar since March.

"Pro-cyclical currencies started finding some respite as US equities showed signs of life yesterday and the dollar faced a correction after a week-long rally," wrote ING strategists in a note to clients.

"While it is tempting to call for the end of the USD run as the risk environment appears to be stabilizing, caution is warranted," they said.

At 0738 GMT, the dollar index against a basket of currencies was down less than 0.1% on the day at 94.246 but up 1.3% on the week - its biggest weekly jump in nearly six months.

"The re-pricing of global recovery expectations may remain a key narrative in markets for longer as more evidence of rising contagion waves (in particular in Europe) is set to fuel concerns about new lockdown measures and their economic impact," ING said.

EU health officials warned on Thursday of "twindemic", as a surge in COVID-19 cases in Europe risks combining with flu infections.

Britain announced new lockdown measures on Tuesday, while France reported that the number of people in intensive care due to the coronavirus jumped over 1,000 for the first time since early June.

The euro rose 0.1% on Friday to $1.1676, but is down 1.4% on the week.

Although investors remain cautious over the upcoming U.S. elections, a return to the dollar surge of March is not expected.

"The ongoing political battle over the nomination of a new Supreme Court justice has increased investors' sensitivity to US politics and decreased their willingness to expose themselves to dollar moves ahead of the November elections," UBS strategists Gaétan Peroux and Tilmann Kolb said in a note.

"While we expect further USD strength in the short term as the speculative positioning washout continues, we continue to hold a long-term bearish view on the dollar at current overvalued levels," they added.

The yen rose slightly against the dollar to 105.385 , while the Swiss franc gained around 0.1% against the euro. (Reporting by Elizabeth Howcroft Editing by Tomasz Janowski)