The euro climbed against its most major counterparts in the Asian session on Monday, as progress in the rollout of a COVID-19 vaccine and hopes of U.S. fiscal stimulus supported riskier assets.

Shipments of the Pfizer/BioNTech vaccine have begun in the US, with vaccinations beginning today.

Further underpinning risk sentiment was extension of Brexit talks to strike a trade deal between the European union and the U.K.

Prime Minister Boris Johnson and EU Commission President Ursula von der Leyen agreed to "go the extra mile" in coming days to reach deal in order to avert a hard Brexit at the end of the month.

U.S. lawmakers plans to unveil a $908 billion coronavirus pandemic relief plan in two separate bills in a bid to win approval and could be presented as early as today.

One will be a $748 billion proposal, which includes funding for small businesses, the jobless and COVID-19 vaccine distribution.

The second bill will have liability protections for business and $160 billion in state and local aid.

The euro advanced to 1.2157 against the greenback and 126.39 against the yen, after falling to 1.2116 and 125.98, respectively in early deals. The next possible resistance for the euro is seen around 1.25 against the greenback and 128.00 against the yen.

The euro hit a 6-day high 1.0792 against the franc and 4-day high of 1.5499 against the loonie, reversing from its early lows of 1.0776 and 1.5463, respectively. If the euro rises further, 1.10 and 1.56 are possibly seen as its next resistance levels against the franc and the loonie, respectively.

In contrast, the single currency eased off to 1.7090 against the kiwi and is on track to pierce near a 2-week low of 1.7071 seen at the beginning of the Asian session. On the downside, 1.65 is likely seen as its next support level.

The euro edged down to 1.6045 against the aussie from Friday's closing value of 1.6067. The euro is seen finding support around the 1.55 level.

The common currency declined to a 4-day low of 0.9063 against the pound from last week's closing quote of 0.9151. Next key support for the euro is possibly seen around the 0.88 level.

Looking ahead, Eurozone industrial production for October is due in the European session.