Six-time champion Serena, 36, beat German world 101 Carina Witthoft 6-2 6-2, while twice champion Venus saw off Italy's Camila Giorgi 6-4 7-5.

The last time the Americans played each other at a Grand Slam was in the final of the 2017 Australian Open, which Serena won when eight weeks pregnant.

"We'd rather have met later," 17th seed Serena said.

Serena missed the US Open last year, giving birth to daughter Olympia shortly after the tournament started. She reached the Wimbledon final in July.

Chasing a record-equalling 24th Grand Slam singles title, Serena unleashed 30 winners and 13 aces on her way to victory over Witthoft and sealed victory when the German netted a forehand.

While Serena wrapped up her win in one hour seven minutes, it took Venus an extra 45 minutes to beat Giorgi.

"Obviously, it's early in the tournament, so both of us are going to be looking forward to continuing to play better," 16th seed Venus said.

Meanwhile, defending champion Sloane Stephens fought back from a set down to beat world number 134 Anhelina Kalinina 4-6 7-5 6-2 in two hours 46 minutes.

Having lost an enduring opening set in an hour and two minutes, American third seed Stephens broke three times in the second set only to be pegged back to 5-5 by Kalinina after receiving treatment for blisters on her hand.

The 25-year-old eventually closed out the set and, despite going a break down in the first game of the decider, proved too strong for the 21-year-old Ukrainian, who was playing in the main draw of a Grand Slam for the first time.

Stephens, who said she had "two bites of sushi and a slushy" during the 10-minute heat break before the final set, bemoaned the conditions on Arthur Ashe Stadium.

"It was super hot," she added. "I was sweating a lot and it was not ideal conditions, but I am happy to get through.

"I hope that I play a little bit better than today [in the next round], go out and compete hard."

She faces Belarus' Victoria Azarenka next, after the former world number one beat Daria Gavrilova 6-1 6-2.

Ukrainian seventh seed Elina Svitolina also progressed with a 6-2 6-3 win over Germany's Tatjana Maria.

The 21-year-old will play Qiang Wang in the third round after the Chinese beat Romania's Irina-Camelia Begu 6-3 6-1.

And eighth seed Karolina Pliskova recorded a 6-2 6-2 win over Romania's Ana Bogdan. The Czech player will face American Sofia Kenin in the third round.

But Spanish 12th seed and former Wimbledon champion Garbine Muguruza is out after falling to a 3-6 6-4 6-4 defeat by Czech qualifier Karolina Muchova, who will play Australian 18th seed Ashleigh Barty in the third round.