Super Serena believes she is No.1

Serena Williams marched into the second round of the US Open on Tuesday and despite being seeded only fourth at Flushing Meadows, the American is in no doubt she is the world's best player.

"Of course I believe that," said Williams after powering to a 6-1, 6-1 win over Coco Vandeweghe after less than an hour on court. "I think there's a number of players on this tour, a few players who believe that.

"I don't care about the ranking. I've been number one. It's cool. But my thing is just to be the best player. If that means I'm winning and I'm not number one, that's fine."

Her one-sided victory came after sister Venus defeated Bethanie Mattek-Sands in straight sets and young American Sloane Stephens upset Italy's No. 22 seed Francesca Schiavone.

Williams said she was thriving on her mentoring role with the 19-year-old Stephens.

"She's a great person and an amazing player," Williams said.

"She's playing so smooth. She looks like she gives no effort when she plays. She's such a beautiful, beautiful player and yes, I embrace that.

Williams laughed about Stephens pressuring her to becoming involved in a relationship.

"She's always encouraging me not to be single. She's always telling me I'm going to find somebody one day," she said.

"I always tell her no I'm not, and complain about it. She's positive about it. She's my mentor more than anything. She's always upbeat."

Williams started the year saying in Brisbane that she disliked tennis but she had a more optimistic outlook after beating Vandeweghe.

"I love it so much," she said. "I know I can't live without it but one day I'm going to have to let it go. I tell someone, you be careful, I'm going to start loving tennis."

Williams said it was difficult to gauge her form because the strong wind inside Arthur Ashe Stadium made it difficult to find her rhythm.

"I usually gauge the wind by my hair," she said. "If it's really going forward I'm thinking, it's really windy.

"I mean, the match was so weird, the conditions were so tough, I couldn't really play my game. It's not the best opportunity to grade yourself."