WASHINGTON — Senate Republicans on Wednesday narrowly staved off an effort by Democrats to deal the Trump administration’s Russia sanctions policy an embarrassing rebuke.

Eleven Republicans joined Democrats in a vote to enforce sanctions against the corporate empire of an influential ally of President Vladimir V. Putin of Russia, but the effort fell three votes short of the 60-vote threshold required to advance the measure. The vote was 57-42, with one Democratic senator not voting.

The sanctions against companies controlled by the influential oligarch, Oleg V. Deripaska, now seem destined to be lifted this week as part of a deal negotiated by the Treasury Department to reduce Mr. Deripaska’s ownership and control of the aluminum giant Rusal and two linked companies.

Sanctions against Mr. Deripaska personally, which had gone into effect last April, remain in force and would not have been affected by the Treasury Department decision or the Senate measure. Mr. Deripaska’s companies waged an aggressive lobbying and legal campaign against the sanctions last year. The administration first delayed putting sanctions on the companies into effect and then announced last month it would lift them entirely.