WASHINGTON (AFP) - Two Democrats were sworn in on Wednesday (Jan 3) as the US Senate's newest members, trimming the Republican Party's already slim majority in the chamber as President Donald Trump seeks to press his legislative agenda.

Vice-President Mike Pence presided in the Senate as Doug Jones of Alabama and Tina Smith of Minnesota took their oaths of office.

Smith's swearing made history, as it brings the number of female senators to 22, an all-time high.

The former Minnesota lieutenant governor was appointed to replace Democrat Al Franken, who resigned over a series of sexual misconduct allegations.

"I'm looking forward to continuing to be a fierce advocate for Minnesotans, and carrying on the progressive legacy of this seat," she said on Twitter.

Jones, a former prosecutor, won a special election last month to claim a seat long held by Republicans. The post was vacated by Alabama's Jeff Sessions when he became US attorney-general.

Jones's upset Senate victory - the first by an Alabama Democrat in 25 years - does not change the balance of power in the 100-member chamber, but it trims the Republican Party's majority to 51-49.

After taking their oaths to "protect and defend the Constitution of the United States against all enemies, foreign and domestic," the pair walked to the Old Senate Chamber to pose with Pence and their relatives for their ceremonial swearing-in.

Pence was accompanied in the Senate by two former vice presidents, Joe Biden and Walter Mondale, both Democrats.

"It's humbling for me to be in their number," Pence told reporters when asked about the vice presidential trio.

The number of female senators has steadily grown since Rebecca Felton became the first woman to hold the position - for a single day in 1922.

Ten years later, Hattie Wyatt Caraway became the first woman elected to the chamber.