While pushing surplus countries in Europe to boost domestic demand, Mr Lew would also prod others to stretch out their fiscal consolidation "where feasible" as the bloc's economic prospects brightened a little, the Treasury official said.
"It appears that the long recession in the region is coming to a close; euro members are regaining financial stability," the Treasury official said.
(Read more: Will the euro'speak' German or European?)
"Despite progress we have seen European leaders make, domestic demand in the euro area remains below its 2009 low in real terms. The euro area is experiencing the highest levels of unemployment in at least 20 years while disinflation remains an acute concern," the official added.
In France, Mr Lew will meet President François Hollande and Pierre Moscovici, the finance minister, and will press Paris for a "balanced growth strategy" as it embarks on domestic reforms.
In Portugal, Mr Lew is expected to deliver a message of encouragement for a country that is emerging from crisis footing and "has ably navigated a narrow path in securing support for its economic policies as well as support from its official lenders", the Treasury official said.
A Treasury official said Mr Lew's trip would also help advance EU-US trade negotiations, which have been under way for about six months. The Treasury has responsibility for many thorny issues in the talks related to the financial services sector, from market access to regulation.