The sanctions bill passed with rare and overwhelming bipartisan support in Congress last week.
However, in a signing statement, Trump criticized Congress for its "haste" to pass the bill and slammed the measure for including what he called "clearly unconstitutional provisions."
"The bill remains seriously flawed — particularly because it encroaches on the executive branch's authority to negotiate," he argued in a separate statement. "Congress could not even negotiate a healthcare bill after seven years of talking."
He also said his administration expects Congress to "refrain from using this flawed bill."
Trump added, "As president, I can make far better deals with foreign countries than Congress."
He said he hopes Russian-U.S. relations improve so sanctions are no longer necessary. Under the new legislation, he would need congressional approval to lift or modify the sanctions.
His latest tweet is a departure from what Vice President Mike Pence said earlier this week.
"But the president and our Congress are unified in our message to Russia," Pence said on a trip to the country of Georgia.
And Rep. Eric Swalwell, D-California, ridiculed Trump's "bromance" with Putin, tweeting, "Gee, Mr. President - so sorry we got in the way of your bromance with the dictator Putin & won't let you weaken our nation for him. #NotSorry."
"The concerns expressed in the president's signing statement are hardly surprising, though misplaced," McCain said in a statement Wednesday.
In response to the sanctions, Russia demanded the U.S. cut its diplomatic staff.
In a post to his Facebook page Wednesday, Russian Prime Minister Dimitry Medvedev said that the signing of the sanctions bill ended the hope that Russia's relations with the Trump administration would improve and that the U.S. "declared an all-out trade war."