Traders attributed the broad gains to better-than-expected ISM services data and a more than one-year high in oil prices as stocks largely shrugged off Italians' vote against constitutional reform in a Sunday referendum.
The euro surprised by strengthening against the dollar after hitting a 20-month low, while the U.S. dollar index hit its lowest since Nov. 15 in Monday afternoon trade. The strong dollar has been a key component of the so-called postelection Trump rally, as the greenback climbed with higher yields and a better growth outlook.
On Monday, Trump picked Ben Carson for secretary of the Department of Housing and Urban Development. The president-elect also renewed focus on U.S.-China relations in a series of weekend tweets.
"Certainly political headlines are filling the void right now, but I wouldn't lose sight of what's happening in Italy," said Gene Tannuzzo, senior portfolio manager at Columbia Threadneedle's Strategic Income Fund.
For many strategists, near-term moves in the euro-dollar hinge on Thursday's ECB meeting. Traders expect the ECB to extend its asset purchase program beyond March 2017, but are divided over whether the central bank will reduce the monthly purchase amount, also known as tapering.
Analysts are also watching for any comments from the ECB Thursday on the Italian referendum results.
"I think this recovery in the euro is premature. ... If we get through the ECB meeting without tapering, the euro will start going down again," said Lee Ferridge, head of macro strategy, North America, State Street Global Markets.
"Any hint from the Italian establishment that this is going to be a very temporary government, the shorter the time frame for the new technocratic government, the worse for the euro," Ferridge said.
Prime Minister Matteo Renzi said he would resign Monday after the defeat of his reform plan, but Italian President Sergio Mattarella asked Renzi to stay on until Parliament passes the budget, which is expected to be approved within days.
Renzi "was going to modernize the entire political system in Italy. I believe that would have been fantastic if they would have been able to get people to vote for it. … With the 'no' vote it doesn't really mean anything changes," said David Marcus, chief executive officer at Evermore Global Advisors, who has holdings in some European companies' stocks.
"I still think that more structurally, Europe is coming along fine," he said.
European Union third-quarter GDP is due for release Tuesday local time. In the U.S., factory orders and U.S. international trade data for October are due in the morning, as well as third-quarter data on productivity and costs.
Toll Brothers, AutoZone, Bank of Montreal, HD Supply, Michaels Cos., Barnes & Noble Education and Bob Evans are scheduled to release earnings before the bell. After the bell, Dave & Buster's, Oxford Industries, AeroVironment and Analogic are set to report earnings.