During European morning trade, the EURO STOXX 50 edged up 0.18%, France’s CAC 40 gained 0.33%, while Germany’s DAX 30 rose 0.20%.
On Monday, Draghi said the ECB is ready to inject a third round of liquidity into the region’s banks if needed, in order to safeguard the bloc’s recovery.
The comments came after data showed that manufacturing output in the euro zone was weaker than expected this month, but this was offset by an improvement in service sector activity.
Equity markets also found support after New York Federal Reserve President William Dudley defended the central bank’s decision to keep its stimulus program unchanged last week, in comments on Monday.
Dudley said that adjustments to the Fed’s USD85 billion-a-month asset purchase program "need to be anchored in an assessment of how the economy is actually performing”.
Financial stocks were mixed, as French lenders BNP Paribas and Societe Generale rose 0.73% and 0.11%, while Germany's Deutsche Bank dipped 0.05%.
Among peripheral lenders, Italian banks Unicredit and Intesa Sanpaolo gained 0.45% and 0.59%, while Spain's BBVA eased 0.07%.
Elsewhere, Telecom Italia rallied 1.86% after Telefonica agreed to pay EUR324 million to increase its stake in Telco SpA, a holding company that owns 22.4% of Telecom Italia, to 66% from 46%.
In London, FTSE 100 added 0.08%, supported by gains in the financial sector.
Shares in the Royal Bank of Scotland rose 0.31% and HSBC Holdings gained 0.42%, while Barclays advanced 0.53% and Lloyds Banking edged up 0.16%.
Meanwhile, mining stocks were broadly lower. Glencore Xstrata dipped 0.02% and Evraz lost 0.94%, while Polymetal and Randgold Resources tumbled 1.02% and 1.57% respectively.
In the U.S., equity markets pointed to a moderately higher open. The Dow Jones Industrial Average futures pointed to a 0.09% rise, S&P 500 futures signaled a 0.02% gain, while the Nasdaq 100 futures indicated a 0.17% increase.
Later in the day, the Ifo Institute was to release its closely watched report on German business climate. The U.S. was to release private sector data on house price inflation, as well as a report on consumer confidence.