US President Donald Trump has distanced himself from Roy Moore after the Republican suffered a historic defeat for the party in conservative Alabama.
The victory for Democrat Doug Jones narrows the Republican majority in the Senate to 51-49, which could complicate Mr Trump's legislative plans.
Mr Moore's campaign was rocked by allegations of sexual misconduct made by several women, which he denied.
Mr Jones is the first Democrat to win a US Senate seat for Alabama in 25 years.
Mr Jones told reporters at a news conference on Wednesday that he received calls from President Trump, Democratic leader Senator Chuck Schumer and his Republican counterpart, Senator Mitch McConnell.
He said Mr Trump made a "very gracious" phone call and extended an invitation to the White House.
Mr Jones added that he has not yet spoken to Mr Moore, reports BBC.