* Control of both Houses gives Biden scope to push agenda

* Riskier currencies seen outperforming on growth prospects

* Dollar outlooks increasingly mixed

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

LONDON, Jan 7 (Reuters) - The dollar bounced off its lowest levels since 2018 to its highest in a week on Thursday, its gains attributed partly to safe-haven buying after violence on Capitol Hill and profit-taking by investors who had been betting on the euro.

The dollar index, which measures the U.S. currency against a basket of peers, rose 0.6% to 89.886.

Hundreds of President Donald Trump's supporters stormed the U.S. Capitol on Wednesday in a bid to overturn his election defeat, battling police in the hallways and delaying the certification of Democratic President-elect Joe Biden's victory for hours.

Broader currency markets were largely unperturbed by the scenes of chaos in Washington, though analysts said the dollar's rise on Thursday indicated some safe-haven buying.

The greenback has declined more than 13% from a March 2020 peak. While dollar positioning still remains bearish, analysts views on the currency's prospects for 2021 are increasingly mixed.

On the one hand, some argue rising inflation expectations based on expected U.S. government stimulus will weigh on real interest rates and put pressure on the dollar, especially with a Federal Reserve that is expected to stand still on rates and allow an inflation overshoot above 2%. Real interest rates are interest rates adjusted for inflation.

Conversely, some analysts say that an extended period of bearish positioning on the dollar, as well as rising Treasury yields, could help lift the currency over the longer term.

"The lift in both nominal yields and inflation expectations provides an interesting backdrop for asset prices," said Jane Foley, head of FX strategy at Rabobank. "As long as real rates are weak the dollar could remain under pressure, particularly given the consensus view that the Fed will allow inflation to overshoot its 2% target."

Foley added that if the market begins to see the U.S. economy as likely to outperform again on growth and begins to suspect that the Fed could be less likely to lean on the yield curve, the dollar could find support.

LONG EURO

She also noted that the market remained long on the euro, and a slow vaccine rollout in Europe could trigger some profit-taking. The single currency sank as much as 0.6% to $1.2245.

Bank of America Merrill Lynch said the long euro market position also makes it "one of the most vulnerable G10 currencies to an overall market risk-off" and that, following the dollar's sell-off last year, Europe's shared currency has now reached a long-term equilibrium.

The Australian dollar slipped 0.83% to 77.39 U.S. cents after touching a nearly three-year high of 78.195 on Wednesday.

The dollar gained 0.6% to 103.64 yen, touching its highest level against the Japanese currency in more than a week.

The yuan was largely flat at 6.4655 per dollar after Chinese authorities signalled a desire for a slower pace of gains.

The remarks by the State Administration of Foreign Exchange (SAFE) on Wednesday follow an advance of around 10% on the greenback since last May as China's economic rebound has led the world's pandemic recovery.

The British pound traded 0.2 lower at $1.3577 as it continued to meander below the almost three-year high of $1.3703 touched on Monday.

Bitcoin marked a fresh all-time high of $37,800 on Thursday, extending a surge of more than 800% since mid-March. It last traded at $37,491. (Reporting by Ritvik Carvalho; additional reporting by Kevin Buckland and Stanley White in TOKYO; Editing by Emelia Sithole-Matarise and Alex Richardson)