WASHINGTON—Lawmakers determined to claim a larger role in foreign policy will challenge President Barack Obama over his nuclear talks with Iran, taking up legislation this week that would give them the power to review—and potentially reject—a final deal.

The bill pits a Congress seeking a larger voice in foreign policy against a White House eager to make its mark on world affairs in its final term in office without congressional interference.

The measure will test lawmakers’ ability to coalesce around a unified position on a major foreign-policy issue. While members of both parties have agitated for more involvement in Mr. Obama’s agenda abroad, they have often found political peril in writing specific legislation and voting on it.

Unlike most other congressional battles Mr. Obama has faced, this time he is encountering significant bipartisan opposition: Democrats intent on avoiding what they view as mistakes made during more than a decade of war in the Middle East and Republicans concerned the president may concede too easily to Iran as negotiators try to reach a final deal by the end of June.

Earlier this month, six world powers including the U.S. reached an agreement with Iran on a framework that would reduce its nuclear capabilities in exchange for easing sanctions. Legislation by Senate Foreign Relations Committee Chairman Bob Corker (R., Tenn.), due for a committee vote Tuesday, would prevent Mr. Obama from easing sanctions on Iran for 60 days after a final deal is reached, during which time Congress could review and potentially vote on the agreement.