The ECB decided to leave its main interest rate at 0.75%.
Although taking no monetary policy action, the ECB and Ireland have reached a compromise on a long-standing dispute over the cost of servicing money borrowed for a failed bank, a source involved in the discussions told Reuters.
Dublin rushed through emergency legislation early on Thursday to liquidate failed Anglo Irish Bank as part of a compromise to avoid paying 3.1 billion euros a year until 2023 on money it took for the stricken lender during a meltdown of the main Irish banks in 2008.
Investors will seek to gauge how much further the euro must rise before its strength forces the ECB to express concern, or even reverse course and contemplate a rate cut.
"The question will now be what tone the news conference will take," said Citi economist Juergen Michels. "We expect the ECB to strike a more cautious tone."
"Recent data has not been exclusively positive," said Michels. "And since the last policy meeting the euro exchange rate has gone up as have short-term money market rates, which the ECB cannot ignore completely."
The euro hit a 15-month peak of $1.3711 on February 1. It traded below that level on Thursday but was up on the day.
French President Francois Hollande said on Tuesday the euro zone must develop an exchange rate policy to protect the currency from "irrational movements".
Erkki Liikanen, an ECB Governing Council member, later dismissed any prospect of the bank pursuing such a policy, saying "we have no foreign exchange target" -- a line ECB chief Draghi is likely to echo.
Draghi can also expect to be bombarded with questions about how much he knew about the derivatives scandal at Siena's Monte dei Paschi bank, and what he did about it when he headed Italy's central bank from 2006 to 2011.
Italy's third largest and oldest bank has been at the centre of a financial and political storm as a result of facing losses of about 1 billion euros from a series of derivatives and structured finance trades and a 9-billion-euro acquisition of smaller rival Antonveneta which left it badly weakened.
Draghi's news conference offers reporters their first chance to quiz him directly on the scandal since his role came into focus late last month.
He faced criticism then after former Italian economy minister Giulio Tremonti said it was "stupefying" that in his role as supervisor of Italy's banking system Draghi failed to discover or prevent loss-making derivatives trades at Monte Paschi.
Monetary policy should prove easier for Draghi to handle.
A batch of indicators cited by Draghi at his January 10 news conference show the economic distortions of the euro zone debt crisis are starting to correct themselves, with the data flow positive over the last month.
One of the indicators shows the ECB's balance sheet shrinking after banks jumped at the chance late last month to repay early 137 billion euros in long-term loans they took from the central bank.
This market-driven unwinding of ECB crisis funding measures is in stark contrast to the expansionary policies being pursued in the United States and Japan.
However, a by-product of that could be to drive the euro yet higher.