WASHINGTON — Senate leaders said they had reached an agreement late on Monday to approve new sanctions against Russia for interfering in the 2016 presidential election and for the country’s conduct in Ukraine and Syria, delivering a striking message to a foreign power that continues to shadow President Trump.

The bipartisan measure would place the White House in an uncomfortable position, arriving amid sweeping investigations into ties between Mr. Trump’s associates and Russia. The sanctions package would also cut against the administration’s stated aim to reshape the United States’ relationship with Russia after Mr. Trump took office.

In a statement released late Monday, the top Republican and Democratic senators on the Foreign Relations Committee and the Committee on Banking, Housing and Urban Affairs said the agreement would impose new sanctions and “provide for a mandated congressional review” if the White House sought to ease penalties unilaterally.

The new sanctions would be imposed upon “corrupt Russian actors,” people involved in human rights abuses, suppliers of weapons to the government of President Bashar al-Assad in Syria and people conducting “malicious cyberactivity on behalf of the Russian government,” among others.