Trump had said earlier this month he would choose a nominee within two weeks of his inauguration.
"We will pick a truly great Supreme Court justice," Trump told reporters who asked about the vacancy as the president signed paperwork to advance construction of the Keystone XL and Dakota Access oil pipelines. Both projects had been blocked under former President Barack Obama.
"Sometime next week," Trump said about his timeline for naming someone to fill the nearly yearlong vacancy created by the February 2016 death of conservative justice Antonin Scalia. "Probably making my decision this week, we'll be announcing next week."
During the campaign, Trump released a list of 20 names of people he said he would consider for a lifetime appointment to the nation's highest court. Before he was sworn in to office, he asserted that potential court appointments were among the reasons he defeated Democrat Hillary Clinton in the election.
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"I think the people of this country did not want to see what was happening with the Supreme Court, so I think it was a very, very big decision as to why I was elected," Trump said at a January 11 news conference at New York's Trump Tower.
Besides taking steps to advance construction of the oil pipelines, subject to renegotiation of the agreements, Trump also signed a notice today requiring the materials for the pipelines be constructed in the United States, though it was unclear how he planned to enforce the measure.
"From now we are going to start making pipelines in the United States," he said.
Trump has sought to focus his first full week in office on jobs and the economy. Republicans, as well as some unions, have cited the pipeline projects as prime opportunities for job growth.
The pipeline would run from Canada to Nebraska where it would connect to existing lines running to US refineries on the Gulf Coast.
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